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# A Loan Market with Inflation

## Game Description

Inspired by Hazlett (2008),1 each student has a private rate of return on a $100 investment, but only half of each group have$100. Equilibrium loan repayment amount is determined the intersection of lenders’ minimum acceptable and borrowers’ maximum acceptable repayment amounts. Payoff for a round (year) equals a player’s increase in real wealth.

After equilibrium convergence in a no-inflation environment, the instructor can add inflation: either certain inflation (to demonstrate the Fisher effect) or uncertain inflation.

### Learning Objective 1: Equilibrium Interest Rate

Supply and demand determine the equilibrium interest rate. Absent investment-return uncertainty, those with the lowest opportunity cost lend to those with the highest real return on investment.

### Learning Objective 2: Fisher Effect

The nominal interest rate (approximately) equals the real interest rate plus the inflation rate. Thus, a change in certain inflation has a predictable effect on nominal interest rates, and no effect on real interest rates.

### Learning Objective 3: Effects of Inflation Uncertainty

With nominal repayment amount fixed, higher than expected inflation reduces the real value of the loan repayment, harming lenders and benefiting borrowers. With lower than expected inflation, the higher than anticipated real value of the repayment harms borrowers and benefits lenders.

In addition, inflation uncertainty reduces the volume of loans if agents are risk averse.

## Brief Instructions

Payoffs (i.e., real returns) are denominated in ore, which should help students distinguish between real and nominal amounts. Borrowers care about how much of their ore production they must sell in order to repay their loans in dollars. Potential lenders, who can either produce or lend, care about how much ore a loan repayment will purchase. The ore price at the beginning of the year is $1 per oz, but the real value of the loan repayment depends on the ore price at the end of the year ore price. The repayment on the$100 loan is determined by market equilibrium. Each round, those with $100 specify the minimum loan repayment amount at which they lend. Those without$100 specify the maximum loan repayment amount at which they are willing to borrow. The equilibrium repayment amount, in dollars, is determined by the intersection of supply and demand.

Those borrowing are now able to produce. They (automatically) sell the ore necessary to make the loan repayment, and keep the rest. For those endowed with $100, those who did not lend will now produce. Those lending take the loan repayment and (automatically) purchase as much ore and possible. By default, the real returns for those endowed with$100 range from 101 to 105 units of ore, and for those without $100 real returns range from 103.5 to 109.5. The equilibrium real interest rate is 4.5% (i.e.,$104.5 repayment on a \$100 loan when inflation is zero), with approximately 80% of subjects either taking or making a loan.

After approximately 3 rounds with Inflation Rate (%)=0, most groups should converge to the equilibrium repayment rate. Between rounds, you may want to point out that deviating from truthful revelation of maximal or minimal repayment amount will have at best a negligible effect on the equilibrium repayment amount.

## Key Treatment Variations

After equilibrium convergence without inflation, introduce certain inflation. As students will be familiar with choosing a repayment threshold equal the value of their production of ore, setting Rounds=2 will be sufficient for most groups to converge to a nominal interest rate approximately equal to the real interest rate plus inflation. We recommend setting Inflation Rate (%)=5 (i.e., 5%).

You can now introduce uncertain inflation. Each of the possible rates you enter happen with equal probability. We recommend making it easy for students to figure out that the expected rate of inflation equals the inflation rate from the certain inflation game. For example, if the previous game had Inflation Rate (%)=5, use 2, 5 and 8 percent for this game. Setting Rounds=4 or 5 so that both sides get to win and lose when the actual rate of inflation does not equal the expected rate of inflation.

## Results

We present results on the nominal interest rate in each market. Shaded lines represent shifts in the underlying values and opportunity costs that arise from inflation. When there are multiple inflation levels possible these shaded lines will be based on risk neutral borrowers and lenders.

We also present results on the average number of transactions across all markets in each round.

The table provides a summary of the relevant equilibrium benchmarks, outcomes-per-group, and average statistics.

Finally, we present a scatter plot for submitted minimum and maximum repayment amounts relate those to the induced minimums and maximums. Systematic deviations from equilbrium predictions (when inflation is zero or predictable) are likely due to overstating minimum and maximum repayments.

1. Hazlett, Denise (2008). “A Classroom Inflation Uncertainty Experiment.” International Review of Economics Education, 7(1): 47–61.