Shapiro–Stiglitz theory

Key takeaways

Shapiro–Stiglitz theory belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Shapiro–Stiglitz theory to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Shapiro–Stiglitz theory from memory before moving on to harder problems.

Reference excerpt

In labour economics, Shapiro–Stiglitz theory of efficiency wages (or Shapiro–Stiglitz efficiency wage model) is an economic theory of wages and unemployment in labour market equilibrium. It provides a technical description of why wages are unlikely to fall and how involuntary unemployment appears. This theory was first developed by Carl Shapiro and Joseph Stiglitz.

Introduction When full employment is achieved, if a worker is sacked, he automatically finds his next job soon. In the circumstances, he does not need to exert his effort in his job, and thus full employment necessarily motivates a worker to shirk provided that he is happy with loafing on the job. Since shirking makes a firm's productivity decline, the firm needs to offer its workers higher wages to eliminate shirking. Then all firms try to eliminate shirking, which pushes up average wages and decreases employment. Hence nominal wages tend to display downward rigidity. In equilibrium, all firms pay the same wage above market clearing, and unemployment makes job loss costly, and so unemployment serves as a worker-discipline device. A jobless person cannot convince an employer that he works at a wage lower than the equilibrium wage, because the owner worries that shirking occurs after he is hired. As a result, his unemployment becomes involuntary.

No-shirking condition Suppose utility is a function of wages w and effort e like u ( w , e ) = w − e {\displaystyle u(w,e)=w-e} , and workers maximize the utility function with a discount rate r. Then let b be the probability per unit time that a worker is dismissed from his job, and now we introduce the expected lifetime utility V u {\displaystyle V_{u}} of an unemployed individual. Then we find the asset value of employment during a short interval [0, T]

V e = w T + e − r T [ b T V u + ( 1 − b T ) V e ] , {\displaystyle V_{e}=wT+e^{-rT}[bTV_{u}+(1-bT)V_{e}]\;,}

because the worker is either dismissed or kept employed during the time. The exponential function appears, because the occasion of dismiss in the interval is once and Poisson distribution is used for the discount rate. Due to the short interval, we approximate the exponential function by 1-rT

V e = w T + ( 1 − r T ) [ b T V u + ( 1 − b T ) V e ] , {\displaystyle V_{e}=wT+(1-rT)[bTV_{u}+(1-bT)V_{e}]\;,}

and simple calculation yields

V e = w T + b T V u − r b T 2 V u r T + b T − r b T 2 , {\displaystyle V_{e}={\frac {wT+bTV_{u}-rbT^{2}V_{u}}{rT+bT-rbT^{2}}}\;,}

lim t → 0 V e = w + b V u r + b . {\displaystyle \lim _{t\rightarrow 0}V_{e}={\frac {w+bV_{u}}{r+b}}\;.}

Then we find the fundamental asset equation of a worker:

r V e = w + b ( V u − V e ) . {\displaystyle rV_{e}=w+b(V_{u}-V_{e})\;.}

For a nonshirker the equation is

r V e , N = w − e + b ( V u − V e , N ) , {\displaystyle rV_{e,N}=w-e+b(V_{u}-V_{e,N})\;,}

and for a shirker

r V e , S = w + ( b + q ) ( V u − V e , S ) , {\displaystyle rV_{e,S}=w+(b+q)(V_{u}-V_{e,S})\;,}

where q is the probability per unit time that a worker is caught shirking and sacked. Then we see

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Shapiro–Stiglitz theory

Start with the simplest possible case. Write down what Shapiro–Stiglitz theory claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Shapiro–Stiglitz theory before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Shapiro–Stiglitz theory ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Shapiro–Stiglitz theory

In research: Shapiro–Stiglitz theory appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Shapiro–Stiglitz theory in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Shapiro–Stiglitz theory is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1984 in economic history, 1984 introductions, Microeconomic theories, so understanding it makes those chapters shorter.
In everyday life: Look for Shapiro–Stiglitz theory outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study Shapiro–Stiglitz theory in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Shapiro–Stiglitz theory means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Shapiro–Stiglitz theory out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Shapiro–Stiglitz theory in simple terms?

In labour economics, Shapiro–Stiglitz theory of efficiency wages (or Shapiro–Stiglitz efficiency wage model) is an economic theory of wages and unemployment in labour market equilibrium. It provides a technical description of why wages are unlikely to fall and how involuntary unemployment appears.

Why does Shapiro–Stiglitz theory matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Shapiro–Stiglitz theory?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Shapiro–Stiglitz theory.