Nowcasting Turkish GDP with MIDAS: Role of Functional Form of the Lag Polynomial

Transcription

1. Nowcasting Turkish GDP with MIDAS : Role of Functional Form of the Lag Polynomial Mahmut GÜNAY February 2020 Working Paper No: 20/02
2. © Central Bank of the Republic of Turkey 2020 Address: Central Bank of the Republic of Turkey Head Office Structural Economic Research Department Hacı Bayram Mh. 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 TURKISH GDP WITH MIDAS : ROLE OF FUNCTIONAL FORM OF THE LAG POLYNOMIAL Mahmut Günay1 ABSTRACT In this paper, we analyze short-term forecasts of Turkish GDP growth using Mixed DAta Sampling (MIDAS) approach. We consider six alternatives for functional form of the lag polynomial in the MIDAS equation, five to twelve lags of the explanatory high frequency variables and produce short-term forecasts for nine forecast horizons starting with the release of data for six months before the start of the target quarter to the release of the data for the last month of the quarter. Our results indicate that functional form of the lag polynomials play non-negligible role on the short-term forecast performance but a specific functional form does not perform globally well for all forecast horizons, for all lag lengths or for all indicators. Import quantity indices perform relatively better until first month’s data for the target quarter become available. As data accumulate for the monthly indicators for the target quarter, real domestic turnover and industrial production indicators stand out in terms of short-term forecasting performance. When all of the three months’ realizations for the monthly indicators become available for the quarter that we want to forecast, unrestricted MIDAS type equations with around five lags with real domestic turnover and industrial production indicators track the GDP growth relatively successfully. ÖZET Bu çalışmada, MIDAS yaklaşımı ile kısa dönemli GSYİH büyümesi tahminleri incelenmektedir. MIDAS denklemi kapsamında, açıklayıcı değişkenlerin beşten on ikiye kadar gecikmeli değerleri kullanılmış, bu gecikmeli değerlerinin katsayılarının modellenmesi için altı farklı fonksiyonel form değerlendirilmeye alınarak tahmin edilmek istenilen çeyrekten altı ay öncesine ilişkin verilerin açıklaması ile çeyreğe ilişkin tüm verilerin tamamlanmasına kadar geçen süreç için dokuz ayrı tahmin üretilmiştir. Gecikmeli değerler için tanımlanan fonksiyonel form kısa dönemli tahmin performansında önemli rol oynayabilmektedir. Ancak, tüm tahmin ufukları, gecikme değerleri ve değişkenler için belirli bir fonksiyonel form en iyi sonucu vermemektedir. Sonuçlar, tahmin edilmek istenilen çeyreğe ilişkin ilk veriler açıklanana kadar ithalat miktar endeksinin görece daha iyi tahminler ürettiğine işaret etmektedir. Çeyreğe ilişkin veriler biriktikçe, sanayi sektöründeki reel cirolar ile sanayi üretim endeksi göstergeleri tahmin performansı açısından öne çıkmaktadır. Bir çeyreğe ilişkin tüm veriler tamamlandığında ise beş gecikme kullanan kısıtlanmamış MIDAS tipi bir denklem ile sanayi sektöründeki reel cirolar ile sanayi üretim endeksi ile üretilen tahminler GSYİH büyümesine oldukça yakın bir hareket sergilemektedir. JEL classification: C53; E37 Keywords: GDP forecasting; MIDAS; polynomial form. 1 Central Bank of the Republic of Turkey. Research and Monetary Policy Department. Istiklal Cad. No.10 06100 Ulus/Ankara,TURKEY. E-mail: mahmut.gunay@tcmb.gov.tr The views and opinions presented in this paper are those of the author and do not necessarily represent those of the Central Bank of the Republic of Turkey or its staff. Author thanks to the anonymous referee and the Editor for the constructive comments and recommendations which help to improve the final version of the paper. 1
4. Non-technical Summary Forecasting key macroeconomic variables such as inflation , unemployment and GDP growth is an integral part of the real-time policy making process. These indicators have their own peculiar characteristics that should be taken into account in the forecasting process to obtain timely, accurate and robust forecasts. There are two issues that have to be taken care of for short-term GDP forecasts: mixed frequency and publication lags. GDP data are available at the quarterly frequency while indicators like industrial production and surveys are available on a monthly basis. This type of a data set, which is composed of quarterly and monthly indicators, is dubbed as mixed-frequency. Second issue is about publication lags. GDP data for a given quarter are published around two months after the end of the quarter while monthly indicators become available on a more timelier basis but, for hard data such as industrial production, with a certain lag as well. Therefore, depending on the timing of the forecasts, there may be missing data for the monthly indicators too. One of the methods that can deal with mixed frequency issue and publication lags is MIDAS approach that enables one to use monthly indicators for forecasting GDP growth. In this paper, we analyze the short-term forecasting performance of MIDAS approach for various indicators such as industrial production, trade indices, taxes, sales and credit. We analyze a total of thirty indicators. Specifying a MIDAS equation requires choices about the lag length of the monthly indicators and the functional form for modelling those lags. We analyze effect of these specifications by using eight different lags and six functional forms. Forecasts are produced starting with the release of data for the six months before the start of the quarter to the release of the all of the three months’ data for the quarter by taking into account what would a forecaster observe at the time of forecasting. Our results indicate that functional form of the lag polynomial plays non-negligible role on the short-term forecast performance but a specific functional form does not perform globally well for all forecast horizons or for all indicators. Lag length structure of the high frequency indicator also affects the results. Our results indicate that before any realization is observed for monthly data for the target quarter, import quantity indices performs relatively well. Once data start to accumulate for the quarter that we want to forecast, real domestic turnover and industrial production indicators provides the best forecasts. Visual inspection of the short-term forecasts of the best performing specifications show that they can track the developments in GDP quite successfully. 2
5. 1 . INTRODUCTION In this paper we analyze forecast performance of Mixed DAta Sampling (MIDAS) approach for short-term forecasts of Gross Domestic Product (GDP) growth for Turkish economy for the period of 2014Q2-2019Q1. Our results indicate that modelling specifications in the MIDAS approach, in terms of the combination of functional form of the lag polynomial and the lag length, affect the forecast performance but there is not a unique specification that performs best for all indicators and for all forecast horizons. Depending on the forecast horizon, different indicators stand out in terms of forecast performance as well. So, while MIDAS approach can effectively deal with mixed frequency and publication lag issues, it is important to analyze the sensitivity of the forecast performance to the modelling choices before using MIDAS type equations for forecasting Turkish GDP growth. GDP provides a comprehensive view about the state of economic activity. Hence, developments in the GDP growth are closely monitored by policy makers and market participants. Yet, GDP data are available at quarterly frequency with a publication lag that can range from 30 to 60 days, and in some cases longer, depending on the country. This means that decision makers that use GDP growth as an input will not be able to utilize the GDP data for the quarter in which they are making decision. Indeed, nowcasting is coined as a term to reflect the fact that forecasts of GDP series should be produced in the reference quarter due to publication lags (Banbura et al. ,2012). Several methods have been developed for producing early predictions of GDP growth. A branch of the forecasting literature concentrates on developing techniques to utilize information content of high frequency indicators such as monthly industrial production or weekly credit data in real time. Two issues that have to be resolved for this aim is to deal with the so-called ragged end issue at the end of the sample stemming from missing data for the high frequency indicators due to publication lags and mixed frequency nature of the data. In order to put the discussion in a more concrete set up, consider the case that industrial production data for February are published in April. Since March figure for industrial production would be missing in April, updating the forecast for the first quarter’s GDP after the announcement of February industrial production would require handling incomplete data for the target quarter, i.e. the quarter that we want to forecast. A reading of the literature shows that initially bridge equation approach was used to utilize mixed-frequency data for short-term forecasts of GDP growth. In this approach, in order to address the issue of publication lags, missing monthly data are forecast using auxiliary models, such as simple AR models. Then these monthly indicators are converted to quarterly frequency and OLS 3
6. regressions are used to estimate coefficients and obtain forecasts (Baffigi et al. (2004) and Diron (2008)). In the given example, March industrial production growth can be forecast with an AR model, then quarterly average of the industrial production can be obtained by combining realizations for January and February with forecast of March. This quarterly growth for industrial production can be used to update the forecast for the first quarter’s GDP growth. In a seminal paper, Giannone et al. (2008) show that it is possible to estimate factors for a mixed frequency data set using Kalman filter after expressing the system in the state-space form. Their findings show that as data accumulates for a given quarter, nowcast errors decline. Several studies tested the performance of factor models for various countries and found promising results for nowcasting with factor models. Over time, in addition to bridge equations, factor models became a popular tool for forecasting teams. In the meantime, Ghysels et al. (2004) developed another method for utilizing mixed frequency data for modelling financial variables. They call this approach as MIDAS. In a nutshell, instead of averaging the higher frequency variable to match the frequency of low frequency variable, as in the case of bridge equations, one regresses low frequency variable onto higher frequency variable. For instance, Ghysels et al. (2006) estimate weekly volatility using daily returns. They use up to 50 lags of the daily indicators. Clements and Galvao (2008 and 2009) conjectured that while MIDAS approach is in general used for financial applications, it is indeed well suited to the task of nowcasting GDP growth. They use several monthly indicators for nowcasting quarterly US GDP growth. Subsequent studies analyzed the performance of MIDAS approach for different countries and it is now included in the toolkit of short-term forecasts of some central banks. A defining characteristic of MIDAS approach compared to other techniques that can deal with unbalanced data sets is that forecast equations are set up in the spirit of direct forecasting rather than forecasting missing values of the higher frequency indicators (see for example Schumacher (2016)). Innovation in the MIDAS approach is to express coefficients of the lags of the higher frequency indicators via a polynomial form. So, even if a researcher uses 50 lags of a daily indicator, only two or three parameters for a polynomial needs to be estimated. Then, coefficients can be obtained using this polynomial. Exponential Almon and Beta are two popular functional forms for lag polynomial. For the case of quarterly GDP and monthly indicators, since the number of lags that are need to be estimated are limited compared to financial applications that use daily data, it is suggested that rather than using a polynomial form, unrestricted coefficient estimates can be used as well which is named as U-MIDAS 4
7. (Foroni et al. 2015). In this paper, we analyze the nowcasting performance of several indicators for Turkish economy using MIDAS approach paying particular attention to the functional form of the lag polynomial. Table 1. Polynomial Forms Used in the MIDAS Applications Year of Publication 2008 2009 Exponential Authors Target Variable Beta Almon Clements, Galvao US GDP + Clements, Galvao US GDP + Marcellino, 2010 Schumacher German GDP + Kuzin, Marcellino, 2011 Schumacher Euro Area GDP + Andreou, 2013 Ghysels,Kourtellos US GDP + 2013 Galvao US and UK GDP + + 2013 Guerin, Marcellino US GDP + Kuzin, Marcellino, GDP for USA, UK, Japan, Germany, 2013 Schumacher France, Italy + Andrade, Fourel, 2014 Ghysels, Idier Euro Area Inflation Risk + + Bessec, 2014 Bouabdallah US GDP + 2014 Foroni, Marcellino Euro Area Macro Variables + Götz, Hecq, 2014 Urbain US Inflation + Barsoum, 2015 Stankiewicz US GDP + Baumeister, 2015 Guerin, Kilian Oil Prices + Foroni, Marcellino, 2015 Schumacher US GDP + 2015 Ghysels, Ozkan US Fiscal Variables + Götz, Hecq, 2016 Urbain US GNP + Jansen, Jin, de GDP for Euro Area, Germany, France, 2016 Winter Italy, Spain, Netherlands + 2016 Schumacher Euro Area GDP + 2016 Smith UK Unemployment Aastveit, Foroni, 2017 Ravazzolo US GDP + Duarte, Rodrigues, 2017 Rua Portugal Private Consumption + + Foroni, Guerin, US Inflation, Ind. Prod. and Personal 2018 Marcellino Cons. Exp. + 2018 Kim, Swanson Korean GDP + 2018 Tsui, Xu, Zhang Singapore GDP + Hepenstrick, GDP for Several Developed and 2019 Marcellino Emerging Economies 2019 Knotek, Zaman US Financial Variables + + 2019 Kurz-Kim Euro Area GDP 2019 Şen-Doğan, Midiliç Turkish GDP Notes: Polynomial form used in the cited paper is denoted by “+” and highlighted with grey shading. 5 UMIDAS + Stepfun Almon + + + + + + + + + + + + + + + +
8. A review of the literature shows that there is not a consensus about the appropriate polynomial form to be used for MIDAS type regressions (Table 1). We see that MIDAS is mainly used for short-term forecasts of GDP but there are applications for inflation and unemployment rate as well. In terms of the polynomial form used, it is seen that exponential Almon dominates the list. Unrestricted-MIDAS (U-MIDAS) became relatively more popular over time. There are some applications that use Beta type polynomials. Almon or step function type weighting are either rarely used or are not employed at all. Most of the papers utilize one or two form of polynomials. So, we contribute to the literature by analyzing the effect of polynomial form on the forecasting performance in a comprehensive way. Şen-Doğan and Midiliç (2019) use MIDAS based models for short-term forecasting of GDP growth in Turkey. Our study differs from this study in a number of ways. First of all, Turkish Statistical Institute (TURKSTAT) made major a revision in the GDP series. After the revisions in the GDP figures, level of GDP increased around 30 percent. Real growth rates changed considerably as well. Revisions to the data set is not limited to the GDP data. TURKSTAT made a substantial revision in the industrial production index as well. In addition to the revisions in the key macroeconomic variables, another difference of the present study is the composition of the data set structure. While Şen-Doğan and Midilic (2019)’s data set is mainly composed from daily financial series, our study looks at the so-called “hard-data” which are monthly indicators. We consider a wide range of indicators from production, turnover, foreign trade, sales, credit and public finance indicators. Analyzing the nowcasting performance of these widely monitored indicators is expected to inform forecasters and policy makers more about the forecasting power of these monthly indicators. Finally, Şen-Doğan and Midiliç (2019) note that Almon polynomial delivered the best results for their analysis while we explicitly present the effect of functional form of lag polynomial on the short-term forecast performance. Our results indicate that depending on the forecast horizon, best performing specifications change in terms of the indicator, functional form of the lag polynomial and lag length of the high frequency indicator. Functional form of the polynomials play relatively more role for the shorter forecast horizons. Analyzing the best performing specifications across indicators show that Beta type polynomials perform relatively better than the popular exponential Almon. Increasing the lag length causes a deterioration for the performance of U-MIDAS while using around five lags makes U-MIDAS a competitive functional form. For longer forecast horizons, import quantity indices perform relatively better. As data accumulate for the target quarter, real domestic turnover and industrial production stand out in terms of short-term forecast performance. Analysis of the short-term forecasts of the best performing specifications show that they can track the developments in GDP quite successfully. 6
9. Structure of the paper is as follows. Next section discusses MIDAS methodology in more detail, then we introduce the data set used in the paper. After presenting forecast exercise design, we discuss results and then conclude. 2. METHODOLOGY: MIDAS REGRESSION APPROACH In this section, we present details about the estimation of the equation used for nowcasting with MIDAS. Before going into technical details, we give some intuition. As pointed out by Schumacher (2016), MIDAS and the bridge equations are extensions of distributed lag models that enable us to work with a data set that is composed of indicators with different frequencies, such as monthly and quarterly. In the so-called bridge equation approach, a higher frequency indicator is converted to lower frequency by appropriate transformation, for example for flow variables by taking average. Then, this transformed series is used in a regression with quarterly GDP to estimate coefficients with ordinary least squares. Innovation in the MIDAS approach is to use all the indicators in their own frequency. Broadly, it can be thought of regressing, say, a quarterly variable onto a growth rate of the monthly indicator for a given number of months. Initially, MIDAS is developed for financial data where a monthly/weekly variable is regressed on a daily indicator. Since there are around 20 working-days in a month, this type of regression requires estimating a lot of coefficients. Ghysels et al. (2004) offered a solution to the parameter proliferation problem. They suggest that using certain functional form of the lag polynomial to estimate the coefficients. So, estimating 20 coefficients for daily observations can be reduced to estimating a few polynomial parameters. After giving intuition, we present bridge equations. Based on this exposition, we will move to MIDAS approach. Using bridge equations, one can link monthly data with quarterly data as in the following equation (Angelini et al. (2011)) :