The success of commercial banks that make loans often hinges on how quickly the bank recognizes that a loan will result in a default (loss). The longer the bank delays in this recognition, the more vulnerable the bank. A paper in the Journal of Accounting Research (June 2015) investigated the extent to which the delayed expected loss recognition (DELR) of a bank is associated with the bank's liquidity risk. Liquidity risk (Yt) was defined as the rate of change of a bank's liquidity with the market in quarter t. DELR (X1,t) was measured as the increase in variation explained in current loan loss provisions in quarter t from adding current and future changes in nonperforming loans over and above lagged changes in nonperforming loans. Several other variables were measured, including loan growth (X2,t, percentage change in loans over quarter t), market-to-book ratio in quarter t(X3,t), and consumer outstanding loan rate (X4,t, total consumer loans outstanding divided by total loans outstanding in quarter t).
a. Write a regression model for liquidity risk at quarter t as a linear function of DELR in the previous quarter.
b. Add loan growth, market-to-book ratio, and consumer outstanding loan rate to the model, part a. Assume that liquidity risk at quarter t is linearly related to the values of these variables at the previous quarter.
c. Add terms to the regression model that will account for quarter-to-quarter variation within a year.