Mixed data sampling (MIDAS) regressions allow us 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. We discuss the pros and cons of unrestricted lag polynomials in MIDAS regressions. We derive unrestricted-MIDAS (U-MIDAS) regressions from linear high frequency models, discuss identification issues and show that their parameters can be estimated by ordinary least squares. In Monte Carlo experiments, we compare U-MIDAS with MIDAS with functional distributed lags estimated by non-linear least squares. We show that U-MIDAS performs better than MIDAS for small differences in sampling frequencies. However, with large differing sampling frequencies, distributed lag functions outperform unrestricted polynomials. The good performance of U-MIDAS for small differences in frequency is confirmed in empirical applications on nowcasting and short-term forecasting euro area and US gross domestic product growth by using monthly indicators.

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The purpose of the Working Papers is to disseminate the results of research conducted by CIRANO research members in order to solicit exchanges and comments. These reports are written in the style of scientific publications. The ideas and opinions expressed in these documents are solely those of the authors.Les cahiers de la série scientifique visent à rendre accessibles les résultats des recherches effectuées par des chercheurs membres du CIRANO afin de susciter échanges et commentaires. Ces cahiers sont rédigés dans le style des publications scientifiques et n'engagent que leurs auteurs.CIRANO is a private non-profit organization incorporated under the Quebec Companies Act. Its infrastructure and research activities are funded through fees paid by member organizations, an infrastructure grant from the government of Quebec, and grants and research mandates obtained by its research teams. Le CIRANO est un organisme sans but lucratif constitué en vertu de la Loi des compagnies duQuébec. Le financement de son infrastructure et de ses activités de recherche provient des cotisations de ses organisations-membres, d'une subvention d'infrastructure du gouvernement du Québec, de même que des subventions et mandats obtenus par ses équipes de recherche. CIRANO Partners -Les partenaires du CIRANO Corporate Partners -Partenaires corporatifs Autorité des marchés financiers Bank of Canada Bell Canada BMO Financial Group Business Development Bank of Canada Caisse de dépôt et placement du Québec

We propose a new Vector Autoregressive identification scheme that enables us to disentangle labor supply shocks from wage bargaining shocks. Identification is achieved by imposing sign restrictions on the responses of the unemployment rate and the labor force participation rate to the two shocks. According to our analysis on United States data over the period 1985–2014, labor supply shocks and wage bargaining shocks are important drivers of output and unemployment both in the short run and in the long run. These results suggest that identification strategies used in estimated new Keynesian models to disentangle labor market shocks may be misguided.