Consumer Choice in Residential Mortgage Market: An Islamic Mortgage Contract

Abstract

This paper examines the Islamic mortgage contract of Diminishing Musharakah and its impact on consumer welfare, house purchase, and mortgage payments. We build both static and dynamic models to study a homeowner’s decision-making. We pay special attention to expectation formations and simulate the model to analyze both Islamic and Conventional mortgage holders’ responses to changes in income growth, house prices, and interest rates. Estimates of the model, using housing data set of U.S. economy (1990–2018), indicate that Diminishing Musharakah contract holders achieve 2.5 to 4% higher discounted utility under constant and declining learning expectations. The reducing balance feature of the Diminishing Musharakah contract provides relative protection to a consumer from adverse income shocks and high-interest rate environments. Simulation results suggest that under dynamic conditions, the Diminishing Mushrakah provides 3.4% lower mortgage cost per housing unit. It prevents consumers of average and low-risk appetite from relatively riskier housing decisions. We learn that consumer chooses a 2.5% smaller house size under Diminishing Musharakah. The model also examines consumers with vector autoregressive (VAR) based expectations. We find that homeowners with optimistic forecasts may achieve a higher utility in a conventional mortgage.

Keywords:

• Diminishing partnership
• Islamic finance
• mortgages
• profit-loss sharing
• utility

Notes

1 It is a partnership agreement between an Islamic bank and customer to contribute towards the financing of the venture. Profits are shared based on pre-agree ratio whereas the loss are shared based on equity contribution. In the context of Diminishing Musharakah the Islamic bank’s ownership in the house entitles them to receive the mortgage rate. In case of default, however, any proceeds from the sale of the house would be shared between the Islamic bank and the customer in line with their ownership proportion. Diminishing Musharakah (DM) is the most popular house financing product used by Islamic Banking Industry. In Islamic countries like Malaysia, Bahrain, Pakistan and other middle eastern countries more than 80% of all housing financing carried out through Islamic banks is based on DM. DM are mostly variable rate mortgages. Although DM can be structured using fixed rates, it seems to be more of a rarity, partially because interest rates are volatile in many Islamic countries. Also the inflation is significantly higher in these countries than the United States. Typically, DM mortgages range from 20 to 25 years. Mostly Islamic banks adopt a rigorous screening criteria to minimize their probability of default. There is limited government protection in case of default. The pricing is risk-based as customers with high probability of default have to pay higher mortgage risk premiums. Many of the Islamic countries also offer conventional products which are similar to those available in the US.

2 It is an agreement for the leasing of property or commodity for a fixed period of time at pre-determined rent.

3 For further details please see Section 2. In this paper, the word ‘conventional’ is used to refer to traditional mortgages which do not follow the rules of Islamic finance.

4 In this paper we have assumed mortgage holders form adaptive expectations (constant or declining learning). Rational expectation (RE) models have been criticized because they fail to take into account the role of lagged dependent variables in empirical data. Slobodyan and Wouters (2012) evaluated forecasting models with empirical data and found adaptive learning models to fit better than RE models. Similarly Marcet and Nicolini (2003) study shows that shifting from fully rational expectation towards quasi rational learning allowed the model to simulate results which better matched with behavior of actual economies.

5 Due to the availability of comprehensive data sets on real estate prices, rent and mortgages, our study analyses American homeowner’s contract selection. Muslim economies, where DM is widely popular, do not have sufficient time-series observations to permit dynamic simulation of our model.. Moreover, the 2008 financial crisis has provided evidence that non-traditional mortgage contracts can be marketed and implemented in the US economy. From 1995-2005, there was a huge increase in the issue of new hybrid mortgage contracts that were primarily promoted to minorities (Blacks and Hispanics) (Hernández-Murillo et al., 2011). Data on multicultural diversity in mortgage markets indicates that upcoming borrowers from Hispanic and Black Community are younger, earn less and have less experience in the home ownership process(Bond et al., 2003). Therefore, DM contract could be offered to the Muslim minority in the US as well as those who may prefer its structural uniqueness.

6 In our paper, a conventional consumer is an individual who has chosen an adjustable-rate mortgage to finance her housing needs.

7 In our model each consumer periodically derives its utility from consumption of non-durable goods and housing services. For further detail please see Section 4.1.

8 It is based on “learning theory” approach in macroeconomics. It indicates that economic agents (assumed to be dynamic optimizers) in a model make decisions based on expected future incomes, employment, inflation and taxes etc. The expectation formation is based on adaptive approach where decision variables are forecasted using time-series econometric techniques. As time progresses, the economic agents in the model re-estimate and reformulate expectations when new data becomes available. (Evans & Honkapohja, 2012).

9 New facts and figures related to decision variables such as inflation and mortgage rate are periodically introduced in our dynamic model.

10 VAR expectations based on US data of 1990-2018 were introduced in our model. It caused the consumer to become highly optimistic about her future trajectory of income growth, house price and mortgage rates.

11 A conventional mortgage has two main categories; fixed and adjustable rate. It is, in essence, a loan of fixed maturity taken by the consumer to purchase a house or land. The fixed-rate mortgage is a loan with a fixed installment amount to be paid in each period. Regardless of the change in market rates, the borrower pays the same instalment amount in the entire mortgage term. In adjustable rate mortgages, consumer payments are subject to change with market rates. The consumer of the contract bears the risk of market changes and benefits if the interest rate falls, requiring him to pay less to the bank. In US, conventional mortgages generally refer to fixed rate mortgages (FRM). We have taken adjustable rate mortgages to be more relevant in comparison to DM’s characteristic. We also generated results in comparison to FRM in Appendix 4.

12 The linkage of rental payments with interest is purely intended to provide a safeguard role against inflation. Certain authors have recommended that Islamic Banks should link rental payments with House Price Index or Rental Index to avoid any connection with interest.

13 Diminishing Musharakah is similar to constant amortization mortgage with respect to principal payment being constant but it has the additional feature to charge a different interest payment on the outstanding loan balance in each period. If the interest rate is made fixed in DM, then according to our model, both of them will have similar cash flows. The major difference arises in the case of default where in the constant amortization mortgage the bank will sell the property to cover up all interest and payments due. In the case of Diminishing Musharakah, upon default the bank can only claim their part of the ownership from the sale of the proceeds and not the entire outstanding amount.

14 The model considers a mortgage term of 30 years. We also run a 5 year mortgage model simulation (see Appendix 5).

15 Following Sommer and Sullivan (2018) the size of the house enters the utility function through ${ S}_t$ and indirectly through $C_t.$ In line with the previous literature (see Chambers, Garriga, and Schlagenhauf (2009 a, c, b)), we have assumed that houses are large structures that can be purchased at a market price $q_t$ per unit of housing. The model assumes there is a linear technology that transforms one unit of owned housing stock, $h_t,$ into one unit of shelter services $s_t.$ Households may consume that one unit of shelter service, meaning they are using the house themselves. The literature assumes that if an individual is living in a bigger house, their personal house service consumption is greater which generates more utility for them. Alternatively, one could also rent out some portion of the house. A bigger house may also allow the individual more potential rental income. In cases of both personal consumption or rent out of the housing unit the customers would experience a utility gain. For larger house size, the sheltered services would be greater which means more personal consumptions and greater utility. The tradeoff, however, is that a bigger house maybe accompanied by a larger mortgage payment which may offset the utility.

16 In our paper remortgaging refers to the process of mortgage holder wishing to move to a house of different size. It is not synonymous to refinancing. The contract of conventional mortgage is an adjustable rate mortgage. At the end of each year, the new loan amortization schedule is calculated based on the remaining principal and current financing rate. As a result, there is no need for refinancing under the conventional mortgage or DM contract in our model.

17 There is only one proportional tax included in the model and that refers to the property tax which is applied at 1% on house prices. The purpose of adding property tax is to incorporate a significant recurring cost in homeowner’s decision making. Higher taxes cause borrowers to choose relatively smaller houses. The tax incentives especially in US tend to differ based on whether individuals opt to become homeowners, landlords or renters. There is no preferential tax treatment based solely on consumer’s mortgage contract selection. As a result, the model has not tax incentives in home ownership, rental services and mortgage payments.

18 The ability to rent out is based on the excess square footage available in a house. We also ran the simulations using the discretized housing sizes where$h_t$ could only be rented in portions of 0.25. The results are found to be robust.

19 Renting out the extra space of the house acts as an investment opportunity for consumer to purchase a bigger house on mortgage and earn additional income. In the model house purchase decision captures both personal and speculative motive. However, our model’s focus is not to analyze the tenure decision of consumers. We focus on understanding the utility difference among homeowners who apply for different mortgage contracts. None of the houses have been bought on mortgage solely to receive rental income or enhance residential investment. The option to rent out has been incorporated in the model to provide an additional feature to enhance the homeowner’s income while applying for a home loan that fulfils shelter needs.

20 The consumption of households is determined by dividing the disposable income (after paying for mortgage installment) by general price level. Each period, the general price levels increase based on inflation rate. High inflation rate in our model reduces the overall consumption of real goods in that period. Moreover, house prices and savings rates in each period are based on US data which also reflect the inflationary impact.

21 $I_{h_{t-1}\ne h_t}$=1 if the consumer changes her house size and 0 otherwise. Consumer in the model also incurs a transactional cost of buying and selling property${(\tau }_b,$ ${\tau }_s$) due to the costly nature of shifting to a new house.

22 The constraints have been placed to filter banking consumers who prefer to become homeowners by applying for a mortgage.

23 In both contracts we have assumed no equity payments at origin. Incorporating this restriction in the model would not affect the outcome of our results because the equity payment requirements in both contracts are similar. DM is not typically 100% LTV (loan to value). Based on the risk appetite of Islamic financial institutions and the customers, it tends to vary. Our model considers LTV to be exogenous and is determined at the start of the contract. It is not allowed to vary and plays a purely mechanical role. Therefore, the results of our model are robust to changes in LTV. We changed LTV to 80% and 70% in our model and found the results to be robust. The objective of this paper is to study difference in utilities caused purely by contract selection. Adding LTV options or making LTV dynamic would cause utility difference to arise out of lender’s policy preferences rather than from the structural feature of the product itself.

24 Static simulations were conducted by inputting the parameter values of Table 3 in the base line model discussed in Section 4. Total Utility (${TU}_t$) of both consumers is simulated for 30 years by computing the optimal levels ($h_t, m_t,$$k_t, s_t)$ decided by the homeowner in each period. We resort to numerical optimization to calculate values that will ensure maximized discounted utility and satisfy the constraints of the model for both consumers. Based on these optimal levels, we project the mortgage payment (${\mathit{pmt}}_t)$ and consumption ($C_t)$ trajectories in each period for both consumers. In static settings, we have also calculated consumer’s utility response (see Figure 2) to changes in mortgage rates (${rm}_t$).

25 Following Sommer and Sullivan (2018) we have not captured default in our model rather the model allows the option to shift towards a smaller house. In certain circumstances this could be considered as a form of default. The literature on housing models with micro-foundations, there is varying preference for the option to default. The literature on housing models with micro-foundations varies on their preference for modeling the option to default. Certain models have placed the option to default but kept the utility cost of default so high that none can actually default (see Guren et al.,2018). In our model we have assumed high utility cost of default to prevent household defaulting. This is because our main focus is to analyze the consumer welfare and bank perspective is included as a supplementary.

26 DM contract can be useful for banks to finance high value risky housing projects. The contract’s payment plan allows bank to systematically recover the principal amount at a faster pace and divert the funds whenever necessary towards other profitable projects.

27 Income tax simulations have been shown in Appendix 2.

28 The model assumes that if the individual wants to apply for remortgage at any time, she can only do so for the remaining period left from the thirty-year original mortgage.

29 To estimate the dynamic responses of consumer’s utility, we input the initial parameter values of Table 3 in our model and use numerical optimization software to calculate the optimal levels ($h_t, m_t,$$k_t, s_t$) for the next 30 periods that will maximize consumer’s utility. In the next period, new data values related to income growth, saving rate and mortgage rate etc., become available to the consumer. She reformulates her expectations about the future using Eq. 15-20 and then recalculates her optimal levels for the next 29 periods. This exercise continues in each period until the completion of contract. We also introduce labor income shocks (See Section 6.2.2) in our model and compute the utility response in both contracts.

30 We also added the option of remortgaging (See Appendix 2) to provide the consumer more discretion in decision making. Similar utility difference are observed as before in Figure 4 except after period twenty five, consumers of both contracts tend to shift towards a smaller house and focus more towards consumption. The reason for such a change is primarily attributed to the fact that the model assumes individual’s life consumption is limited to thirty years.

31 keeping $h_{t }=1.$

32 If remortgaging option is provided to consumer then compared to Figure 5 simulations indicate that in period seventeen, there is a sudden decline in utility difference curve (see Appendix 2) because both consumers remortgage to smaller house. Conventional consumer moves to a relatively much smaller house. High property prices and rising mortgage rates encourage consumers to sell their bigger homes, pay off their mortgage and invest the additional capital in high interest bearing accounts.

33 In initial periods a conventional consumer’s payments will primarily be of interest, with a small portion of principal included. As the mortgage matures, principal portion of the payment will increase and interest portion will reduce. The interest payment in each period is charged by multiplying the current market rate with the outstanding principal balance of the mortgage.

34 In DM contract, the equity balance of bank reduces at a uniform rate and therefore makes the consumer less vulnerable to market rate changes.

35 After Period 15, the influence of an income shock is reduced due to the lower number of periods left in the mortgage.

36 One of the major concerns for any mortgage contract is failure to pay. It will primarily arise when a consumer experiences severe disutility from paying mortgage installments due to reduced income. Therefore, our focus has been to analyze consumer response in adverse conditions.

37 The values indicate that there will be a series of negative income shocks in the housing market and the intensity of each shock will be 90% of the previous year effect. The value of d has been placed 0.1 to ensure that income growth rate ($y_t$) converges to approximately 0% at the end of 30 year period.

38 $y_t$=income growth; $\Delta {rm}_t$= annual change in mortgage rate; ${\Delta rd}_t$= annual change in savings rate;${\Delta p}_t$=annual change in rental prices;$\Delta q_t$=annual change in house price per unit; $\Delta {Pr}_t$= annual general price inflation.

39 $A_1 \mathit{and}$ $A_2$ are a 6 × 6 matrix of coefficients. $\epsilon$ is 6 dimensional white noise process.

40 High risk consumer tends to select a relatively bigger house in Islamic mortgage because model calculations indicate that the utility derived from consumption in later periods is significantly higher. She is willing to pay higher instalment in the early periods to reap greater rewards in future consumption.

41 S&P Dow Jones Indices LLC, S&P/Case-Shiller U.S. National Home Price Index [CSUSHPINSA], retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/CSUSHPINSA, August 8, 2019.

42 Payment schedule differences between DM and conventional mortgage are provided in Appendix 6.

43 The initial parameters values are not synonymous to steady state values. In each period, the parameter values; house prices, mortgage rate, inflation, savings rate and income growth change based on the actual US household data and then mortgage holders optimize their decisions accordingly. Whereas the rest of the parameters mentioned in Table 3 have been held constant. The requirement was to have a complete 30-year period data set. Therefore, the paper started the analysis from the year 1990 where the mortgage rates were on average around 10.13%. So only for the year 1990 does our model take the rate of 10.13%. Since we are not simulating a fixed rate mortgage therefore the rate would change in our model based on real time changes in the data. Also, it is important to note that in our model the agent is not optimizing all 30 periods at a steady state rate, rather she is reevaluating her decision in each period, every time a new rate emerges in the market.

44 The model’s endogenous variables are $h_t, m_t,$$k_t, s_t { C}_t$ and the exogenous variables; $q_t,{rm}_t,\delta ,\theta ,{\tau }_b,{\tau }_s,w_t,{rd}_t,\sigma , \alpha ,{\beta }_t\mathrm{ }, P{r}_t.$ From these exogenous variables $\delta ,\theta ,$${\tau }_b,{\tau }_s,$$\sigma \mathit{and} \alpha$ remain constant. They have been taken from literature as averages for the US economy. Even if these variables change, they do not significantly influence the findings of the model because its impact on both contract holders is similar.

45 Source: Freddie Mac, 30-Year Fixed Rate Mortgage Average in the United States [MORTGAGE30US], retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/MORTGAGE30US, August 8, 2019.

46 Source: U.S. Bureau of Economic Analysis, Real Disposable Personal Income [A067RL1Q156SBEA], retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/A067RL1Q156SBEA, August 8, 2019.

47 Source: U.S. Bureau of Economic Analysis, Personal Saving Rate [PSAVERT], retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/PSAVERT, August 8, 2019.

48 The housing size $h_t$ is determined endogenously in our model based on the parameter values set on the market conditions. It is not derived directly from empirical data.

49 In later periods, contract holder’s income is expected to be higher and therefore results in more consumption ($C_t)$ especially if they have to make lower mortgage payments.

50 The payment schedule is based on the purchase of a house worth $300,000 on mortgage.

51 The payment schedule is based on the purchase of a house worth $300,000 on mortgage.