Assignment Task
The purpose of this assignment is to apply variable selection methods and time regression and statistical tests to come up with an appropriate econometric model for interest-bearing deposits using aggregate deposit data of FDIC-insured financial institutions in the US. The data is divided in two subsets. The first subset consists of actual data (“scenario=actual”) on bank deposits and other variables (real disposable income growth, housing price index, fiveyear treasury rates and the state-level unemployment rate) that are potential explana-tors of deposits recorded quarterly from 1984 to end of 2016. The second subset consists of quarterly forecast data from the first quarter of 2017 to the first quarter of 2020 for the candidate explanatory variables under three premises for the state of the US economy: baseline growth, adverse, and severe economic downturns. Consider the following econometric models of interest-bearing deposits:
Y = Xβ + Xlβl + Xllβll + Xlllβlll + Xllllβllll + ut
∆Y = ∆Xθ + ∆Xlθl + ∆Xllθll + ∆Xlllθlll + ∆Xllllβllll + et
%∆Y = ∆Zλ + ∆Zlλl + ∆Zllλll + ∆Zlllλlll + ∆Zllllλllll + %∆W γ + %∆Wlγl + %∆Wllγll + %∆Wlllγlll + %∆Wllllγllll + vt
where Y represents interest-bearing deposits, X is composed of the the intercept and candidate right-hand side variables (rdi, ur, treas 5y and hpi) listed in the table below, and the subscript l is a time (quarterly) lag such that Xll represents a two-quarter lag of X and ∆Zllll represents a four-quarter lag of ∆Z. For equation (3), Z includes all variables originally measured in percentage rate (e.g., unemployment rate) while W represents the remaining (non-percentage) variables. β − βllll, θ − θllll, λ − λllll and γ − γllll are model parameters to be estimated and ut , et and vt are error terms.
Based on the first subset of data provided (1984-2016), you are to do the following tasks:
1) Transform the deposit data as necessary to create the dependent variables for models (1)-(3)
2) Undertake the following transformations:
- create one to four-quarter lags of the candidate explanatory variables in the table below.
- create one-quarter differences of the the explanatory variables and their lags (one to four quarter lags)
- create one-quarter percentage changes of the the explanatory variables and their lags (one to four quarter lags) 1
3) Create quarterly dummies and add them to the dataset to control for potential seasonality.
4) Graph each of the three dependent variables over time to detect evidence of a trend.
5) Check if deposits (levels only) exhibit seasonality.
6) Test for a unit root in each of the three dependent variables using the augmented Dickey Fuller test and four lags (since the data is measured quarterly).
7) Based on the results of the unit root tests and evidence of trends, suggest what would be the best transformation for the dependent variable (ideposits). That is, use the statistical evidence to choose between the three models above. Then, use the forward variable selection model (with a selection entry cutoff of 10%) and the set of candidate explanatory variables (including their relevant transformations computed in 2) to come up with a subset of variables that best explain the behavior of interest-bearing deposits for the chosen specification. If there is evidence of seasonality in the data, be sure to force quarterly seasonal dummies into the model. Be sure to refine your variable selection if one or more VIFs for the variables exceed 10.
8) For the chosen model, test for normality of the residuals, autocorrelation of the residuals (Godfrey or Durbin-Watson tests), and heteroscedasticy of the errors.
9) Report your parameter estimates along with Newey-West robust standard errors in one table.
10) Use the forecast data (2017-2020) for the explanatory variables to conduct an out of sample prediction of the amount of interest-bearing deposits for the chosen model specification for each economic growth scenario (baseline, adverse, and severe).
11) Finally, graph actual vs. in-sample predicted values of deposits for the actual sample period (1984-2016) and the out of sample predictions for 2017-2020.
Background
In general, it is expected that rising rates will incentivize customers to move deposit balances from non-interest-bearing deposit products (e.g., demand deposit accounts) into interestbearing products (e.g., money market accounts). Furthermore, significant rate increases may incentivize some customers to be selective as to which interest-bearing deposit products they choose. For instance, certificates of deposit (CDs) typically offer higher rates than other interest-bearing deposit products and, depending on the rates offered, customers may elect to hold excess balances in CDs. However, CDs require that customers deposit their money at the bank for an agreed upon term, with early withdrawals typically resulting in a penalty. Similarly, other interest-bearing deposit products typically have requirements that must be met in order for customers to earn the offered rate, e.g., minimum balance requirements. Given these considerations, the impact of interest rate changes on deposit balances and mix, e.g. how much is held in interest-bearing versus non-interest-bearing, is often not clear cut.
Since banks use deposit balances as a core source of funding (banks need deposits to make loans and earn interest on those loans), there is a strong need to understand the underlying drivers of deposit behavior and factors that impact deposit balances and mix. Using industry deposit data available from the FDICs quarterly banking profile (https://www.fdic.gov/bank/analytical/qbp/) and economic data available from FRED (https://fred.stlouisfed.org/), the RMA team would like help in determining the impact of changes in interest rates, and other economic factors, on industry deposit balances and deposit mix over time. The insights gleaned from this industry study can help inform banks’ internal deposit models and potentially bring to light factors currently not being considered.