Forecasting charge-off rates with a panel Tobit model: the role of uncertainty

ABSTRACT

Based on a large panel dataset of small commercial banks in the United States, this paper employs a dynamic panel Tobit model to analyse the role of uncertainty in forecasting charge-off rates on loans for credit card (CC) and residential real estate (RRE). When compared to other standard predictors, such as house prices and unemployment rates, we find that the effect of uncertainty changes on charge-off rates is more pronounced. Furthermore, it is evident that including heteroscedasticity in the model specification leads to more accurate forecasts.

KEYWORDS:

• Loan charge-offs
• panel data
• Tobit model
• forecasting

JEL CLASSIFICATION:

• C11
• C23
• C53
• G21

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

¹ The small-size banks are defined to be those banks that have total assets of less than one billion dollars.

² The raw data can be downloaded from https://www.chicagofed.org/banking/financial-institution-reports/commercial-bank-data. The charge-off rates are calculated as dividing charge-offs by the stock of loans. See the online appendix of Liu, Moon, and Schorfheide (2019) for the details of data construction.

³ The data along with the computer codes are available for download from: https://web.sas.upenn.edu/schorf/working-papers/.

⁴ The reader is referred to the computer codes available at to obtain the measures of uncertainty: https://sites.google.com/site/hmumtaz77/research-papers?authuser=0.

⁵ The variables include: real personal income and its components (social insurance, dividends, benefits and other income), overall employment, unemployment rate, real house prices, non-performing loans and net assets of banks, leading indicator, coincident indicator, all employees in health and education, financial services, government, information, leisure and hospitality, manufacturing, non-farm, professional and business services, and other services.

⁶ There are 12 observations in each sample: one observation for the initialization of estimation, 10 observations for the estimation sample, and one observation for the evaluation of forecast.

⁷ For the model specification M, we report the average log predictive scores $LP{S}_h\left(M\right)=\frac{1}{N}\sum _{i=1}^{N}ln(\mathbb{I}\left\{Y_{iT+h}=0\right\}{\mathbb{P}}_{Y_{1:N,0:T}}^{Y_{iT+h}}\left\{Y_{iT+h}=0|M\right\}+\mathbb{I}\left\{Y_{iT+h}>0\right\}p\left(Y_{iT+h}|Y_{1:N,0:T}\right)$ and the continuous ranked probability scores $\mathrm{C}\mathrm{R}\mathrm{P}{\mathrm{S}}_{\mathrm{h}}\left(\mathrm{M}\right)=\frac{1}{\mathrm{N}}\sum _{\mathrm{i}=1}^{\mathrm{N}}\underset{0}{\overset{\mathrm{\infty }}{\int }}{\left({\mathrm{F}}_{{\mathrm{Y}}_{1:\mathrm{N},0:\mathrm{T}}}^{{\mathrm{Y}}_{\mathrm{i}\mathrm{T}+\mathrm{h}}}\left({\mathrm{Y}}_{\mathrm{i}}|\mathrm{M}\right)-\mathbb{I}\left\{{\mathrm{Y}}_{\mathrm{i}\mathrm{T}+\mathrm{h}}\le {\mathrm{Y}}_{\mathrm{i}}\right\}\right)}^2\mathrm{d}\mathrm{y}$ as in Liu, Moon, and Schorfheide (2019).

⁸ We further examined the forecast performances using the uncertainty data of Mumtaz (2018) at longer horizons, i.e. 2-, 3-, and 4-quarter-ahead. The results provide further evidence that the heteroscedastic specifications deliver more accurate forecasts, with these results are not reported but are available upon request.

Additional information

Funding

This study is supported by the National Natural Science Foundation of China under [Grant No. 72022020, 71974181 and 71774152].