Testing Nowcast Monotonicity with Estimated Factors

This paper proposes a test to determine whether `big data' nowcasting methods, which have become an important tool to many public and private institutions, are monotonically improving as new information becomes available. The test is the first to formalise existing evaluation procedures from the nowcasting literature. We place particular emphasis on models involving estimated factors, since factor-based methods are a leading case in the high-dimensional empirical nowcasting literature, although our test is still applicable to small-dimensional set-ups like bridge equations and MIDAS models. Our approach extends a recent methodology for testing many moment inequalities to the case of nowcast monotonicity testing, which allows the number of inequalities to grow with the sample size. We provide results showing the conditions under which both parameter estimation error and factor estimation error can be accommodated in this high dimensional setting when using the pseudo out-of-sample approach. The finite sample performance of our test is illustrated using Monte Carlo simulations, and we conclude with an empirical application of nowcasting U.S. real gross domestic product (GDP) growth and five GDP sub-components. Our test results confirm monotonicity for all but one sub-component (government spending), suggesting that the factor-augmented model may be misspecified for this GDP constituent