Nowcasting and Short-term Forecasting Turkish GDP: Factor-MIDAS Approach

Transcription

1. Nowcasting and Short-term Forecasting Turkish GDP : FactorMIDAS Approach Selçuk Gül Abdullah Kazdal July 2021 Working Paper No: 21/11
2. © Central Bank of the Republic of Turkey 2021 Address: Central Bank of the Republic of Turkey Head Office Structural Economic Research Department Hacı Bayram Mah. İstiklal Caddesi No: 10 Ulus, 06050 Ankara, Turkey Phone: +90 312 507 80 04 Facsimile: +90 312 507 78 96 The views expressed in this working paper are those of the author(s) and do not necessarily represent the official views of the Central Bank of the Republic of Turkey.
3. Nowcasting and Short-term Forecasting Turkish GDP : Factor-MIDAS Approach Abdullah Kazdal Selçuk Gül Abstract This paper compares several nowcast approaches that account for mixed-data frequency and “ragged-edge” problems. More specifically, it examines the relative performance of the factoraugmented MIDAS approach (Marcellino and Schumacher; 2010) in nowcasting Turkish GDP with respect to benchmark forecasts. By using 40 monthly indicators in factor extraction, several combinations of the factor-MIDAS models are estimated. Recursive pseudo-out-of sample forecasting exercise in evaluating the alternative models’ performance suggests that factor-augmented MIDAS performs better than the benchmarks, especially in nowcasting. However, they do not provide much information content to forecasting a quarter ahead. Results indicate that taking into account the “ragged-edge” characteristic of the data helps improve the predictive ability of the nowcast models. Besides, dynamic factor extraction methods provide better predictions than the static factor extraction methods. Özet Bu çalışmada, farklı frekanslı veri ve örneklem sonunda eksik veri bulunması problemlerini hesaba katan çeşitli angörü yaklaşımları karşılaştırılmaktadır. Özel olarak, Türkiye’nin GSYİH'sini cari dönemde tahmin etmede faktörle genişletilmiş MIDAS yaklaşımının (Marcellino ve Schumacher; 2010) referans tahminlere kıyasla göreli performansı incelenmektedir. Faktör çıkarımında 40 adet aylık gösterge kullanılarak faktör-MIDAS modellerinin çeşitli kombinasyonları tahmin edilmektedir. Alternatif modellerin performansının değerlendirilmesinde yinelemeli sözde örneklem dışı tahmin çalışması, faktörle genişletilmiş MIDAS'ın, özellikle angörü yaparken, baz model tahminlerinden daha iyi performans gösterdiğine işaret etmektedir. Öte yandan, bir çeyrek sonrasını tahmin etmede çok fazla ilave bilgi içeriği sağlamamaktadırlar. Sonuçlar, verilerin "düzensiz uç" özelliğini hesaba katmanın, angörü modellerinin tahmin yeteneğini geliştirmeye yardımcı olduğunu göstermektedir. Ayrıca, dinamik faktör çıkarma yöntemleri, statik faktör çıkarma yöntemlerinden daha iyi tahminler sağlamaktadır. JEL Classification: C52, C53, E37 Keyword: Forecasting, Mixed Frequency, Factor-MIDAS  Research and Monetary Policy Department, Central Bank of the Republic of Turkey. E-mail: abdullah.kazdal@tcmb.gov.tr Research and Monetary Policy Department, Central Bank of the Republic of Turkey. E-mail: selcuk.gul@tcmb.gov.tr The views expressed in this paper are those of the authors and do not reflect the official views of the Central Bank of the Republic of Turkey. All errors are the authors’ own.  1
4. Non-Technical Summary Given the publication delays in Gross Domestic Product (GDP), policymakers rely on nowcast models that account for all the available information to have a clear and early understanding of the current state of the economic activity. These models mainly use highfrequency indicators such as industrial production, international trade volumes, etc., to forecast the low-frequency variable. However, practitioners generally face problems such as mixed-data frequency and unbalanced datasets. In this study, we apply the factoraugmented MIDAS methods introduced by Marcellino and Schumacher (2010) that account for these problems in nowcasting the Turkish GDP. We estimate several combinations of the model with alternative factor estimation and MIDAS approaches. Then, we evaluate the predictive performance of the alternative models by a recursive pseudo-out-of-sample forecasting exercise. The results of the out-of-sample forecasting exercise suggest that factor-augmented MIDAS performs better than the benchmarks, especially in nowcasting. However, they do not provide much information content to forecasting a quarter ahead. The results indicate that taking into account the “ragged-edge” characteristic of the data helps improve the predictive ability of the nowcast models. 2
5. I . Introduction and Literature Review Policymakers need to have a clear and timely understanding regarding the state of economic activity while taking their policy actions. However, they generally lack current information on the main economic activity indicator, the Gross Domestic Product (GDP), given that the realizations of the data are released with a publication lag of 2-3 months. Accordingly, accurate and on-time projections of the GDP serve as critical inputs for policymakers. In contrast to the delay for the release of quarterly GDP data, many business cycle indicators are more timely and available at higher frequencies, such as the monthly industrial production, international trade volumes, survey data like PMI (the Purchasing Managers Index), and financial data that are published more frequently. Economists benefit from the availability of higher frequency data (monthly, weekly, and even daily) as they may nowcast the GDP with more precision by increasing the frequency of the information regarding the current state of the economic activity. Previous literature provides alternative macroeconomic modeling approaches that can incorporate all the available information in a timely manner to produce early GDP forecasts. However, due to the nature of the high-frequency data, forecasters face challenges regarding mixed-data frequency and publication lags that require tailor-made solutions. For instance, indicators released asynchronously and having different publication lags lead to irregular patterns of missing values at the end of the sample, which is called as ‘raggededge’ problem of data (Wallis, 1986). As an example of the mixed-data frequency problem, GDP is released quarterly, whereas many predictors are sampled at monthly or higher frequencies. Given that, nowcast models that account for mixed-frequency and raggededge data have received substantial attention in the recent period. Among the alternative nowcast approaches, a popular and easy to implement approach to forecast lower frequency variables using higher frequency indicators is the bridge equation models that aggregate higher frequency variables to balance dimension with lower frequency target variable (Barhoumi et al. (2008)). This single equation approach relies on linear regressions in which the dependent variables are generally GDP or its components at a quarterly frequency. The explanatory variables are, however, monthly indicators, aggregated (mostly averaged) at a quarterly frequency, that have the best predictive powers to nowcast those components. One caveat of the bridge equations is that although aggregation of the variables makes the implementation of the forecasting exercise easier, the aggregation of the high-frequency variables have the risk of losing information content of the high-frequency indicators. 3
6. Another modeling framework that can deal with such a mixed frequency data structure is the Mixed-data sampling (MIDAS) model. In the MIDAS regression, a low-frequency variable is regressed on a small number of higher-frequency variables using restricted lag polynomials (Ghysels et al. (2007), Andreou et al. (2010)). Similar to the bridge equations, this approach is also a single-equation approach, but in MIDAS, the aggregation bias is avoided. Pioneering works of Clements and Galvao (2008, 2009) adopted the MIDAS methodology to predict US quarterly GDP with monthly indicators. Additionally, Kuzin et al. (2011) and Ferrara and Marsilli (2013) utilize MIDAS models to predict the Euro area and French GDP, respectively. The data-rich environment made the factor models utilizing information from large datasets become popular in the recent forecasting literature. The main contribution of the factor models is that information content from a large data set can be represented through a few factors providing important gains in terms of degrees of freedom. These factors are used as regressors in the forecasting equation instead of using a large number of indicators as explanatory variables in the model. There is a steadily growing literature on nowcasting Turkish GDP using factor models and, more recently MIDAS approach. Among those, Modugno et al. (2016) nowcasts Turkish GDP employing dynamic factor models with a medium-scale mixed frequency dataset that includes 15 variables. They provide evidence that real variables contribute more to nowcasting GDP than the financial variables. Similarly, using a medium-scale dataset including 19 variables, Soybilgen and Yazgan (2018) nowcast the Turkish GDP and report that the information released after the nowcast horizon does not add to the predictive power. They also show that construction and service sector variables and credit indicators contribute to the accuracy of the nowcasts. To nowcast the annual Turkish GDP, Günay (2018) employs the MIDAS approach. Using industrial production and exchange rates at the monthly frequency and quarterly GDP, he provides evidence that adding exchange rate, a proxy for financial variables, in the dataset improves the nowcast efficiency, especially in the earlier periods of nowcasting. Another study using MIDAS in nowcasting Turkish GDP, Doğan and Midiliç (2019), uses a large dataset of financial variables, specifically 204 daily financial series. They report that financial variables possess information content for the GDP and daily financial indicators lead to an increase in the nowcast performance. Recently, Günay (2020a) examines the role of the functional form of the lag polynomial in estimating Turkish GDP using the MIDAS approach. He documents that although the lag polynomial matters in the nowcasting, there is no “one size fits all” kind of functional form that can be employed in every forecast horizon, lag lengths, and series. Finally, Günay (2020b) examines some practical questions regarding the nowcasts for Turkish GDP. His results suggest that 4
7. filling the missing data , especially financial and survey data, using VARs leads to an increase in the forecast performance. Besides, he provides evidence that benefitting a large number of indicators using the factor model approach has higher performance than forecast combination, a method to pool forecasts. A summary of the literature on nowcasting Turkish GDP provides several results. First, accounting for the mixed structure of the data improves the nowcast performance. Second, against the existence of abundant economic variables, a parsimonious approach generally performs better. Third, the performance of the nowcasts may differ over time depending on the varying performances of specifications, the choice of lag polynomial, and the lag structure of the explanatory variables. Finally, financial variables generally contribute to the nowcast performance. The combination of factor estimation and the MIDAS methods gives the Factor MIDAS (FAMIDAS) approach, as introduced by Marcellino, and Schumacher (2010). In MIDAS methodology, mainly a low-frequency target variable regressed on a set of higherfrequency indicators. In contrast, in the Factor MIDAS approach target variable regressed on estimated factors rather than a small groups of economic indicators. In other words, in the standard MIDAS approach, economic variables at a higher frequency are used as regressors, while in the Factor MIDAS approach the explanatory variables are estimated factors. Given that factors are extracted from a balanced dataset, there are alternative factor estimation methods in the literature. Two popular approaches utilized by practitioners are static principal component analysis (PCA), which is described in Stock and Watson (2002), and dynamic principal component analysis (DPCA) introduced by Forni et al. (2005). However, as discussed above, typically, the real data structure is unbalanced due to the ‘ragged-edge’ problem. Therefore, factor estimation methods that take proper account of these data irregularities are required. In this paper, we follow the methodology of the Marcellino and Schumacher (2010)1 to estimate the factor-augmented MIDAS model that includes factor estimation with alternative methods to deal with the ragged-edge data.2 First, to have a balanced dataset a simple realignment method offered by Altissimo et al. (2006) is employed with the dynamic principal component analysis (DPCA) factor estimator of Forni et al. (2005). Alternatively, the combination of expectation-maximization (EM) algorithm and static principal 1 Examples for forecasting studies that estimate the factor-augmented MIDAS model following the framework of Marcellino and Schumacher (2010) are Ferrara and Marsilli (2019) for global growth, Kurz-Kim (2019) for Euro area GDP, den Reijer and Johansson (2018) for Swedish GDP, Kim and Swanson for Korean GDP, Jansen et al. (2016) for five Euro area countries, and Foroni and Marcellino (2014) for Euro area GDP. 2 We use the Matlab codes used in Marcellino and Schumacher (2010) provided by Christian Schumacher. 5
8. component analysis (PCA) factor estimator of Stock and Watson (2002) is adopted. Finally, the two-step parametric state-space factor estimator based on the Kalman smoother of Doz et al. (2006) is utilized. After the factor extraction step, we use the estimated factors as high-frequency regressors in the alternative MIDAS models. We then compare the forecasts of these alternative MIDAS models with the benchmark estimations in nowcasting Turkish GDP. Recursive pseudo-out-of sample forecasting exercise in evaluating the alternative models’ performance provides several important results. First, taking into account the ragged-edge data provides gains in the predictive ability of the nowcast models. Second, factor-MIDAS specifications perform better than the simple benchmark models, especially for nowcasting. However, they do not provide so much additional information in the forecast period that makes the factor-MIDAS models practical as only nowcasting tools. Third, the dynamic factor estimation method is found to demonstrate better nowcasting performance than the static factor estimation method. The paper proceeds as follows. Section 2 briefly describes the dataset, while Section 3 provides detailed information about methodological aspects of factor estimation approaches with ragged-edge data structure and alternative MIDAS specifications. Section 4 presents the design of the forecast comparison framework and compares the empirical results of the alternative models. Finally, Section 5 summarizes and concludes. II. Data The dataset contains Turkish quarterly GDP growth from 2005Q2 until 2020Q1 and 40 monthly indicators from 2005M2 until 2020M5. It includes indicators from industrial production, car sales, real domestic turnover in the industry, foreign trade quantity indices, electricity production, domestic sales of white goods, transaction volume in credit and debit cards, tax revenues and government spending. Additionally, variables regarding global risk perception indicators and credit growth rates are included (Table A1). Our approach in selecting variables for nowcasting Turkish GDP follows Günay (2020b) that we use common indicators employed in the previous forecasting literature. Specifically, we aim to include indicators from different dimensions of economic activity such as industrial production, private consumption, foreign trade, and public finance. These variables are known to have a high correlation with GDP. While composing the dataset, we have considered the parsimony principle; thus, we kept the number of variables restricted. Besides, following the previous evidence in the literature that financial variables contribute to the nowcast performance, we include the financial variables in the dataset. 6
9. The series are transformed to ensure stationarity and required seasonal adjustments are made. The dataset is final dataset and does not contain vintages of data, as they are not available for Turkey. To be able to take ragged-edge data structure into consideration, we follow the approach adopted by Banbura and Rünstler (2007). We take the data availability structure at the end of the sample and assume that such pattern remained the same for all recursions. More details about the publication scheme and a stylized example for data availability of these variables are provided in Table A2. III. Methodology As mentioned in the previous section, for the first time Clements and Galvao (2008, 2009) utilized MIDAS approach for macroeconomic forecasting. After that, Marcellino and Schumacher (2010) developed the factor-MIDAS approach combining MIDAS approach with factor models to forecast lower variable (GDP), via utilizing information from a large set of higher-frequency indicators.3 To be able to account for unbalanced datasets, they utilize three alternative factor estimation methods. Moreover, to control for the effects of the alternative MIDAS specifications they use three different MIDAS approaches as basic, smoothed and unrestricted. To compare the forecast performance of Factor-MIDAS the authors take single-frequency factor model based on quarterly aggregated data as benchmark. Following the very similar methodology of Marcellino and Schumacher (2010), in our framework consisting large data set and aiming factor forecasting; we follow the two-step procedure similar to Boivin and Ng (2005). Firstly, we estimate factors, and then construct a dynamic model for the predicted variable employing estimated factors. It should be noted that two important issues are dealt with throughout this forecasting exercise as it is done by Marcellino and Schumacher (2010). Firstly, the ragged-edge pattern exists in the data set due to different publication lags while estimating factors should be dealt with. Secondly, after factor estimation, the frequency difference between monthly estimated factors and quarterly GDP data should be addressed via alternative MIDAS models to be able to produce forecasts. III.I. Factor Estimation with Ragged-Ends In a general form, the static factor model representation for monthly observations can be written as follows: