Baking Models

This post is inspired by a comment my professor made in class

I spend an inordinate amount of time thinking about, making and watching content related to food. Not to brag, but my friends agree that it’s paid off.

Model writing is a lot like baking. The flavourings and proportions may be different, but the base still comprises of the same ingredients, the basics instructions are more or less the same. In models, the basic ingredients are a production function and something representing supply and demand. The basic instruction is to maximise profit. We can then flavour the base model by adding more agents, costs/benefits and/or strategic behaviour as needed.

To illustrate this, consider the question of how surplus extracting agents enable corruption. The question itself is incredibly complex, like this.

There is regulation, bureaucracy, information flow or lack thereof, culture….. Ades, Di Tella (1999) presents a model that beautifully captures the concept in the simplest possible terms.

Corruption a la Ades Di Tella

Ingredients

• Economic profits
• Bureaucrat, economically rational
• Moral Costs, distributed on F()
• Wages, stable and punishment
• Probability of Audit

Directions

Take the perspective of the bureaucrat. The bureaucrat will decide whether to be honest or corrupt depending on which yields a higher payoff. If the bureaucrat is honest, he takes home his wage. The utility from honesty is the stable wage.

If the bureaucrats chooses corruption and gets away with it, he’ll get a cut of the profits in addition to the wage. If he doesn’t get away with it, he is forced to take punishment wages. In both cases, the bureaucrat incurs a moral cost. To calculate utility from corruption, first add stable wages to a proportion of economic profits (we suggest 1/2). Multiply the probability of audit by this expression. Next, subtract moral cost from punishment wages. Multiply this by the inverse of audit probability

The bureaucrat will compare the two. Solve for the threshhold wage needed for honesty at a given moral cost.

Any bureaucrat with a moral cost less that m will choose corruption. Moral cost is distributed according to the CDF F(). The probability of corruption is

To find the relationship between profits and probability of corruption, take the derivative with respect to wages

It’s positive! Higher profits lead to a greater probability of corruption.

One could spice up the base model: Add loss aversion, multiple rounds with belief updating, strategic behaviour of firms…..

However, just as the fanciest cake still tastes like cake, adding elements to the model should not change the result: more surplus, more corruption.

So, the next time there’s a model like this

Try to find the basic cake

buried underneath the maths.