Sparse HP filter: Finding kinks in the COVID-19 contact rate.

In this paper, we estimate the time-varying COVID-19 contact rate of a Susceptible-Infected-Recovered (SIR) model. Our measurement of the contact rate is constructed using data on actively infected, recovered and deceased cases. We propose a new trend filtering method that is a variant of the Hodrick-Prescott (HP) filter, constrained by the number of possible kinks. We term it the sparse HP filter and apply it to daily data from five countries: Canada, China, South Korea, the UK and the US. Our new method yields the kinks that are well aligned with actual events in each country. We find that the sparse HP filter provides a fewer kinks than the ℓ 1 trend filter, while both methods fitting data equally well. Theoretically, we establish risk consistency of both the sparse HP and ℓ 1 trend filters. Ultimately, we propose to use time-varying contact growth rates to document and monitor outbreaks of COVID-19.

DESPERATE TIMES CALL FOR DESPERATE MEASURES: GOVERNMENT SPENDING MULTIPLIERS IN HARD TIMES.

We investigate state-dependent effects of fiscal multipliers and allow for endogenous sample splitting to determine whether the U.S. economy is in a slack state. When the endogenized slack state is estimated as the period of the unemployment rate higher than about 12%, the estimated cumulative multipliers are significantly larger during slack periods than nonslack periods and are above unity. We also examine the possibility of time-varying regimes of slackness and find that our empirical results are robust under a more flexible framework. Our estimation results point out the importance of the heterogenous effects of fiscal policy and shed light on the prospect of fiscal policy in response to economic shocks from the current COVID-19 pandemic. (JEL C32, E62, H20, H62).

Estimating a breakpoint in the pattern of spread of COVID-19 in South Korea.

OBJECTIVES: Amid the global coronavirus disease 2019 (COVID-19) crisis, South Korea has been lauded for successfully preventing the spread of this infectious disease, which may be due to the aggressive implementation of preventive policies. This study was performed to evaluate the pattern of spread of COVID-19 in South Korea considering the potential impact of policy interventions on transmission rates. METHODS: A SIR (susceptible-infected-removed) model with a breakpoint that allows a change in transmission rate at an unknown point was established. Estimated trajectories of COVID-19 from SIR models with and without a breakpoint were compared. RESULTS: The proposed model with a break fitted the actual series of infection cases much better than the classic model. The estimated breakpoint was March 7, 2020 and the transmission rate dropped by 0.23 after the breakpoint. A counterfactual study based on our estimate indicated that the number of infected could have reached 2 500 000 compared to the peak of 8000 in the observed series. CONCLUSIONS: It is critical to consider a change in the transmission rate to evaluate the trajectory of spread of COVID-19 in South Korea. Our estimation and counterfactual experiments indicate that public health interventions may play a role in determining the pattern of spread of infectious diseases.

Testing for a Debt-Threshold Effect on Output Growth.

Using the Reinhart-Rogoff dataset, we find a debt threshold not around 90 per cent but around 30 per cent, above which the median real gross domestic product (GDP) growth falls abruptly. Our work is the first to formally test for threshold effects in the relationship between public debt and median real GDP growth. The null hypothesis of no threshold effect is rejected at the 5 per cent significance level for most cases. While we find no evidence of a threshold around 90 per cent, our findings from the post-war sample suggest that the debt threshold for economic growth may exist around a relatively small debt-to-GDP ratio of 30 per cent. Furthermore, countries with debt-to-GDP ratios above 30 per cent have GDP growth that is 1 percentage point lower at the median.

The lasso for high dimensional regression with a possible change point.

We consider a high dimensional regression model with a possible change point due to a covariate threshold and develop the lasso estimator of regression coefficients as well as the threshold parameter. Our lasso estimator not only selects covariates but also selects a model between linear and threshold regression models. Under a sparsity assumption, we derive non-asymptotic oracle inequalities for both the prediction risk and the l1-estimation loss for regression coefficients. Since the lasso estimator selects variables simultaneously, we show that oracle inequalities can be established without pretesting the existence of the threshold effect. Furthermore, we establish conditions under which the estimation error of the unknown threshold parameter can be bounded by a factor that is nearly n-1 even when the number of regressors can be much larger than the sample size n. We illustrate the usefulness of our proposed estimation method via Monte Carlo simulations and an application to real data.