When irrelevant alternatives do matter. The effect of focusing on loan decisions

More related examples can be found in Huber et al. (1982), Simonson (1989), Tversky and Simonson (1993) or Roelofsma and Read (2000). For a detailed review of related experimental findings see for example Camerer et al. (2004). More recently, Bertrand et al. (2010) presented field experiment evidence about how context-specific information changes the decision-maker’s behavior.

For earlier works on this literature see Tversky (1969), Tversky and Simonson (1993), González-Vallejo et al. (1996, 2012), Roelofsma and Read (2000), González-Vallejo (2002) or Scholten and Read (2010).

These approaches have been successful in explaining a range of puzzling observations in different fields of economic decisions. More specifically, the model of Bordalo and his colleagues can account for the decoy effect (Bordalo et al. 2013a), the endowment effect (Bordalo et al. 2012b), the anchoring effect (Bordalo et al. 2014), provides an explanation on how salience leads to a transformation of objective probabilities into probability weights (Bordalo et al. 2012a) and explains several puzzles associated with asset prices (Bordalo et al. 2013b). Furthermore, the model of Kőszegi and Szeidl (2013) explains time-inconsistent behavior, both present bias and overcommitment to future goals at the same time, price sensitivity in health decisions (Abaluck 2011), loan financing without budget constraints (Bertaut et al. 2009; Stango and Zinman 2009) and lump-sum preferences compared to annuity in retirement and health decisions (Brown et al. 2008).

This result is in line with the empirical observation that people tend to underestimate the burden of a loan (Hoelzl et al. 2009; Akers and Chingos 2014).

Notice that we do not restrict our analysis to the case of fair loans only. Throughout the analysis a loan is considered in the most general way as a consumption profile, which can yield negative or non-negative utility to the consumer.

Notice that we do not restrict our attention to alternatives with the same duration as the original plan. Throughout the analysis we allow alternative repayment plans to have shorter duration than the flat plan as far as their present value is the same. In this regard, periods with no installments should be considered as periods with \(x_t=0\).

Prepayment penalties are often used to protect lenders against the financial loss of paid interest over time.

Here we assume that \(\eta _s\) is a lump-sum fee, however, all our results remain valid with the penalty which is based on a percentage of the remaining balance of the loan.

Notice that if the prepayment option is available only from the second period, i.e., \(s>1\), inequality (4) holds for strict inequality. This is because, in this case (4) can be rewritten as \(\delta [g(x_1)-g(x)]x +\sum _{t=2}^{T} \delta ^t \big [g\big (\sum _{t=2}^T \delta ^{t-2} x+\eta _{t}\big )-g\big (\sum _{t=2}^T \delta ^{t-2} x+\eta _{t}\big )\big ]x \ge 0\). Since the first part of this inequality is strictly positive and the second part equals to zero the inequality always holds.

If prepayment penalties are constant over time, i.e., \(\eta _s^{\mathrm{opt}}=\eta \) for every \(s=1,\dots , T-1\) as it is often the case, the optimal prepayment penalty is unique, yet to determine this penalty the same information is needed as in the general case.

Strategic default is possible only with non-recourse loans, when the debt is secured only with the collateral, and in the case of default the lender is not allowed to collect the borrower’s other assets.

Here we are focusing on recourse loans, yet our results hold for non-recourse loans as well.

For example, assuming that the probability of default of a fair loan with flat repayment plan of ten periods is \(10\%\) it would require an unlikely high default cost of roughly eight times greater than the loan to violate this condition.

See, e.g., Loewenstein and Prelec (1992), Camerer et al. (2004), Thaler (2005) and Berns et al. (2007).

For more on quasi-hyperbolic discounting see Laibson (1997).