U-Midas: Midas Regressions with Unrestricted Lag Polynomials

56 Pages Posted: 8 Jun 2016

See all articles by Claudia Foroni

Claudia Foroni

Independent

Massimiliano Giuseppe Marcellino

Bocconi University - Department of Economics; Centre for Economic Policy Research (CEPR)

Christian Schumacher

Deutsche Bundesbank

Multiple version iconThere are 2 versions of this paper

Date Written: 2011

Abstract

Mixed-data sampling (MIDAS) regressions allow to estimate dynamic equations that explain a low-frequency variable by high-frequency variables and their lags. When the difference in sampling frequencies between the regressand and the regressors is large, distributed lag functions are typically employed to model dynamics avoiding parameter proliferation. In macroeconomic applications, however, differences in sampling frequencies are often small. In such a case, it might not be necessary to employ distributed lag functions. In this paper, we discuss the pros and cons of unrestricted lag polynomials in MIDAS regressions. We derive unrestricted MIDAS regressions (U-MIDAS) from linear high-frequency models, discuss identification issues, and show that their parameters can be estimated by OLS. In Monte Carlo experiments, we compare U-MIDAS to MIDAS with functional distributed lags estimated by NLS. We show that U-MIDAS generally performs better than MIDAS when mixing quarterly and monthly data. On the other hand, with larger differences in sampling frequencies, distributed lag-functions outperform unrestricted polynomials. In an empirical application on out-of-sample nowcasting GDP in the US and the Euro area using monthly predictors, we find a good performance of U-MIDAS for a number of indicators, albeit the results depend on the evaluation sample. We suggest to consider U-MIDAS as a potential alternative to the existing MIDAS approach in particular for mixing monthly and quarterly variables. In practice, the choice between the two approaches should be made on a case-by-case basis, depending on their relative performance.

Keywords: mixed data sampling, distributed lag polynomals, time aggregation, now-casting

JEL Classification: E37, C53

Suggested Citation

Foroni, Claudia and Marcellino, Massimiliano and Schumacher, Christian, U-Midas: Midas Regressions with Unrestricted Lag Polynomials (2011). Bundesbank Series 1 Discussion Paper No. 2011,35, Available at SSRN: https://ssrn.com/abstract=2785452 or http://dx.doi.org/10.2139/ssrn.2785452

Massimiliano Marcellino

Bocconi University - Department of Economics ( email )

Via Gobbi 5
Milan, 20136
Italy

Centre for Economic Policy Research (CEPR) ( email )

London
United Kingdom

Christian Schumacher

Deutsche Bundesbank ( email )

Wilhelm-Epstein-Str. 14
Frankfurt/Main, 60431
Germany

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