## Introduction

This course covers research topics related to economic slack. So what is economic slack? Economic slack describes the amount of productive resources in the economy that are unused. There are many different forms of slack: people who cannot find a job and remain unemployed; machines left idle in a factory; employed workers left idle on the job; hotel rooms, restaurants table, airplane seats that remain vacant; durable goods that cannot be sold and depreciate; perishable goods that cannot be sold and perish.

Economic slack represents a waste of productive resources, and it therefore is something that should be limited. Moreover, in addition to its wastefulness, unemployment generates other, large costs to society. People who are unemployed suffer from lower mental and physical health than employed workers. Even employed people in areas with high unemployment report lower well-being. Accordingly, good economic policy should stabilize economic slack at a desirable level and avoid periods of elevated slack.

The course is centered around formal modeling, but it also presents evidence supporting the assumptions introduced in the models. In the course we cover several models of economic slack and use them to answer several questions:

- Why does slack exist?
- How does slack affect economic life?
- Why does slack vary over time?
- How are slack fluctuations related to price and wage rigidities?
- What is the socially optimal amount of slack?
- How should monetary policy respond to cyclical fluctuations in slack?
- How should fiscal policy respond to fluctuations in cyclical slack?
- What happens at the zero lower bound?

##### Introductory video

##### Introductory readings

- Krugman (2000) – This paper argues that uncomplicated models can be helpful. In this course we will develop models that are as uncomplicated as possible—and that are much simpler than models typically studied in graduate macroeconomic courses.
- Frey, Stutzer (2002) – This survey provides evidence that personal unemployment and aggregate unemployment significantly reduce happiness. The evidence refers to the pure effect of unemployment, which controls for the income loss and other indirect effects of unemployment.

## Overview of business-cycle models

This section first reviews the Kuhnian model of science. It then uses the Kuhnian perspective to understand how, over the past century, business-cycle macroeconomics evolved from the IS-LM model (inspired by Keynes’s *General Theory*) to the General Disequilibrium model (with nonclearing markets) to the Real Business-Cycle model (with perfectly competitive markets) and finally to the New Keynesian model (with monopolistically competitive markets).

Modern business-cycle models—both Real Business-Cycle model New Keynesian model—focus on fluctuations in prices and quantities. By contrast, the business-cycle model developed in this course accounts for fluctuations in prices, quantities, and slack. Introducing slack is especially important to study business cycles because slack varies far more than prices over the business cycle. Introducing slack is necessary to study business-cycle stabilization policies because fluctuations in slack have large consequences for welfare.

##### Lecture videos

- Organization of scientific knowledge in paradigms (notes )
- Cycling through paradigms (notes )
- Qualities of a good paradigm (notes )
- Structure of business-cycle models (notes )
- Paradigms of business-cycle research (notes )
- From the Keynesians to the New Keynesians (notes )
- Absence of slack in modern business-cycle models (notes )

##### Readings

- Summers (1986) – This paper discusses the origins and limitations of the Real Business-Cycle model.
- Benassy (1993) – This survey reviews the General Disequilibrium literature.
- Blanchard, Kiyotaki (1987) – This paper develops a business-cycle model with monopolistic competition that is a direct precursor to the New Keynesian model.

## Prevalence of slack and matching function

This section documents the presence of economic slack on the labor market (unemployed workers) and on the product market (idle labor and capital). It also documents that such slack always coexists with vacant jobs and unfulfilled consumption. Then, it introduces the matching function, which is the tool that we will use to model the coexistence of unemployed workers and vacant jobs, and of idle labor and capital and unfulfilled consumption. The matching function summarizes the complex process through which workers searching for jobs meet firms searching for employees, and firms searching for customers meet consumers searching for sellers.

The business-cycle model developed in this course differs from canonical business-cycle models because it applies a matching structure to the labor and product markets. In contrast, the Real Business-Cycle model features perfectly competitive labor and product markets. The New Keynesian model features monopolistic competition on the two markets. And older disequilibrium models feature nonclearing Walrasian markets.

##### Lecture videos

- Prevalence of unemployed workers (notes )
- Other forms of labor market slack (notes )
- Prevalence of idle capacity (notes )
- Other forms of product market slack (notes )
- Prevalence of vacant jobs (notes )
- Prevalence of unfulfilled consumption (notes )
- Matching function and matching market (notes )
- Properties of the matching function (notes )
- Market tightness and trading probabilities (notes )
- Urn-ball matching function (notes )
- Cobb-Douglas matching function (notes )
- Constant-elasticity-of-substitution matching function (notes )

##### Readings

- Petrongolo, Pissarides (2001) – This survey reviews the microfoundations of the matching function, its empirical properties, and its applications.
- Shimer (2007) – This paper generates an aggregate matching function from mismatch in local labor markets.
- Montgomery (1991) – This paper generates an aggregate matching function from wage competition between firms.

## Basic model of slack

This section develops a basic macroeconomic model of slack. The model is static. It is built around a matching function. Because of the matching function, self-employed workers are not able to sell all their services: there is always some slack. Wealth (in the form of real money balances) enters the utility function. People derive direct utility from wealth because wealth is a marker of social status, and people value high social status. Thanks to this assumption, and although the model is static, the aggregate demand is nondegenerate.

##### Lecture videos

- Structure of the basic model (notes )
- Household’s production function (notes )
- Product market and market tightness (notes )
- Idle capacity (notes )
- Matching cost (notes )
- Matching wedge (notes )
- Household’s utility function (notes )
- Household’s budget constraint (notes )
- Definition and properties of the household’s problem (notes )
- Solving the household’s problem (notes )
- Computing the aggregate demand curve (notes )
- Properties of the aggregate demand curve (notes )
- Computing the aggregate supply curve (notes )
- Properties of the aggregate supply curve (notes )
- Price norm (notes )
- Individual and bilateral surpluses from trade (notes )
- Bilateral inefficiencies in Keynesian and New Keynesian models (notes )
- Bilateral efficiency for any price norm (notes )
- Structure of the solution of the model (notes )
- Strategy to solve the model (notes )
- Computing market tightness from the AD and AS curves (notes )

##### Readings

- Michaillat, Saez (2015, sections 1–2) – These sections develop the basic model of slack.
- Diamond (1982) – This paper develops the first matching model of the product market and uses it to study stabilization policy.
- Gourio, Rudanko (2014) – This paper develops a dynamic matching model of the product market. Prices are set through competitive search.

## Model of slack with income and wealth inequality

This section introduces income and wealth inequality in the basic model of slack. We compute the aggregate demand and aggregate supply curves with inequality, and show how the model with inequality can be solved. In the model the marginal propensity to spend varies with slack, and the deviation from Say’s Law appears clearly.

##### Lecture videos

- Prevalence of income and wealth inequality (notes )
- Modeling income and wealth inequality (notes )
- Matching in the heterogeneous-agent model (notes )
- Consumption and saving in the heterogeneous-agent model (notes )
- Unequal consumption and savings in the heterogeneous-agent model (notes )
- Slack-dependent marginal propensity to spend (notes )
- Aggregate supply in the heterogeneous-agent model (notes )
- Aggregate demand in the heterogeneous-agent model (notes )
- Solving the heterogeneous-agent model (notes )
- How much rationality does the model assume? (notes )
- How can a statistical agency predict tightness? (notes )

##### Reading

- Saez, Zucman (2019) – This paper documents the rise of income and wealth inequality in the United States. The data come from distributional macroeconomic accounts.

## Discussion of the solution concept

This section provides additional discussions of the solution concept used in the basic model of slack, and discusses an interesting special case. It also shows how the model solution is the equilibrium (in the sense from physics not economics) of a dynamical model in which households slowly learn the market tightness.

##### Lecture videos

- General structure of the model solution (notes )
- Graphical representation of the model solution (notes )
- Deviation from the model solution (notes )
- Recasting the model in terms of visits (notes )
- Defining the model solution in terms of visits (notes )
- Solving the model in terms of visits (notes )
- Solution of the model in a special case with no matching cost (notes )
- Convergence to the model solution (notes )

##### Reading

- Michaillat, Saez (2015, sections 2D and 2H) – These sections discuss the equilibrium concept in the basic model of slack, and solve the model in the special case with no matching cost.

## Price and wage rigidities

The matching model requires to specify price norms. Theoretically, there are many possibilities. We could assume that prices equilibrate supply and demand while tightness remains fixed. If the tightness is fixed at the right level, the economy is always efficient, in the spirit of a perfectly competitive, Walrasian model. We could also assume that tightness equilibrates supply and demand while prices remain fixed, in the spirit of a fixprice, Keynesian model. In that case, the economy is generically inefficient, either too slack or too tight. Or we could assume something in between, where tightness and prices jointly adjust to equilibrate supply and demand.

This section reviews evidence from microdata and ethnographic surveys. The evidence suggests that prices and wages are not fully flexible but instead somewhat rigid, and that fairness is a key reason behind price and wage rigidities. The section then shows how realistic pricing norms can be inserted into the basic model of slack. It also derives comparative statics in response to aggregate demand and aggregate supply shocks under fixed prices and rigid prices. It contrasts these results to those obtained under bargained prices.

##### Lecture videos

- Setting prices under bilateral monopoly (notes )
- Why are prices not restricted to a narrow price band (notes )
- Frequency of price changes (notes )
- Prevalence of rigid prices (notes )
- Frequency of wage changes (notes )
- Frequency of wage changes for new hires (notes )
- Prevalence of wage rigidity (notes )
- Model solution with fixed prices (notes )
- Comparative statics with fixed prices (notes )
- Bargaining over prices (notes )
- Model solution with bargained prices (notes )
- Comparative statics with bargained prices (notes )
- Model with rigid prices (notes )

##### Readings

- Fabiani, Druant, Hernando, Kwapil, Landau, Loupias, Martins, Matha, Sabbatini, Stahl, Stokman (2006) – This paper argues, based on surveys of more than 11,000 European firms, that prices of goods and services are sticky and that firms do not change prices more often by fear of antagonizing customers, who dislike price changes that they deem unfair.
- Bewley (2004) – This paper provides evidence of wage rigidity. It then argues that firms avoids pay cuts because they damage morale, which eventually reduces productivity, increases turnover, and complicates recruiting.
- Eyster, Madarasz, Michaillat (2021) – Empirically, it seems that pricing norms are shaped by fairness considerations. This paper examines the possible origins of such pricing norms. The paper develops a model of pricing in which buyers care about the fairness of markups, and firms take these concerns into account when setting prices. The model yields price rigidity and realistic Phillips curves.

## Model of slack with labor and product markets

This section presents a model with two markets and two types of slack: a labor market with unemployment and a product market with idleness. Each market is organized around a matching function. Unemployment and idleness interact with each other. For instance, after an increase in aggregate demand, firms find more customers. This reduces the idle time of firms' employees and thus increases firms' labor demand. This in turn reduces unemployment.

In this extended model, not all workers are employed, and not all goods and services produced by firms are sold. The model therefore incorporates the three traditional types of unemployment: Keynesian, classical, and frictional. Unemployment has a Keynesian component because it depends on how easy or difficult it is for firms to sell their goods. It has a classical component because it depends on the real wage. And it has a frictional component because it depends on how costly it is for firms to recruit workers.

Moreover, the comovements between output, employment, product-market tightness, and labor-market tightness observed in the United States through the lens of the model indicate that unemployment fluctuations are caused by fluctuations in labor demand, themselves caused by fluctuations in aggregate demand.

##### Lecture videos

- Structure of the two-market model (notes )
- Matching on the labor and product markets (notes )
- Pricing on the labor and product markets (notes )
- Firm’s recruiting process (notes )
- Firm’s production function (notes )
- Firm’s problem (notes )
- Labor demand and labor supply curves (notes )
- Aggregate demand and aggregate supply curves (notes )
- Structure of the solution of the two-market model (notes )
- Graphical representation of the solution of the two-market model (notes )
- Keynesian, classical, and frictional unemployment (notes )
- Solving the two-market model (notes )
- Aggregate demand shocks with fixed prices (notes )
- Technology shocks with fixed prices (notes )
- Labor supply shocks with fixed prices (notes )

##### Readings

- Michaillat, Saez (2015, sections 3–6) – These sections develop the model of slack with labor and product markets, and assess the sources of unemployment fluctuations in the United States.
- Diamond (2011) – This is Peter Diamond’s Nobel lecture. It discusses the applications of the matching framework to the product market and other markets.
- Wasmer, Weil (2004) – This paper develops a model of slack with labor and financial markets—each organized around a matching function.

## Dynamic model of slack

This section presents a dynamic version of the basic model of slack. In the dynamic model, unemployment is determined by the intersection of an aggregate demand curve, stemming from households' consumption-saving decisions, and an aggregate supply curve, corresponding to the Beveridge curve.

An advantage of moving to a dynamic environment is that interest rates appear into the model. Indeed, the real interest rate is a key determinant of aggregate demand. By setting a nominal interest rate, the central bank can stabilize the economy. The model is therefore useful to study the effect of monetary policy on unemployment—for instance to assess the possibility of a soft landing in the aftermath of the pandemic inflation spike.

##### Lecture videos

- Structure of the dynamic model (notes )
- Matching with long-term employment relationships (notes )
- Law of motion of unemployment (notes )
- Convergence to the Beveridge curve (notes )
- Aggregate supply curve in the dynamic model (notes )
- Recruiting wedge (notes )
- Household’s utility function (notes )
- Household’s budget constraint (notes )
- Household’s problem (notes )
- Price norm and monetary policy (notes )
- Dynamics of the model (notes )
- Aggregate demand curve and solution of the dynamic model (notes )
- Aggregate demand shocks with fixed inflation (notes )
- Aggregate supply shocks with fixed inflation (notes )
- Effects of monetary policy and soft landing (notes )

##### Readings

- Michaillat, Saez (2022, sections 1–4) – These sections develop the dynamic model of slack and perform various comparative statics.
- Michaillat, Saez (2021) – The dynamic model of slack assumes that wealth enters households' utility function. This paper exports this assumption to the New Keynesian model and shows that it is also helpful there. Indeed, the assumption resolves all the anomalies of the New Keynesian model at the zero lower bound. With wealth in the utility function, at the zero lower bound, there is no collapse of output and inflation, and the effects of government spending and forward guidance are bounded and reasonable.
- Ball, Leigh, Loungani (2017) – This paper documents the prevalence of Okun’s law—the negative correlation between output and unemployment rate—in the United States since 1948. Okun’s law implies that output and market tightness are negatively correlated over the business cycle, which in turn implies that aggregate demand shocks are the main source of cyclical fluctuations.

## Social welfare, efficiency, and inefficiency

Unlike in neoclassical models, in matching models the economy generally operates inefficiently. Except in knife-edge cases, there is too much or too little slack. Since the unemployment rate is generally inefficient, it is critical to know whether the current unemployment rate is above or below the efficient unemployment rate.

This section therefore develops a simple formula for the efficient amount of unemployment. It shows that under simple but realistic assumptions, the efficient unemployment rate is the geometric average of the unemployment and vacancy rates: $u^\ast = \sqrt{uv}$. Hence, the economy is efficient when there are as many vacancies as jobseekers, inefficiently tight when there are more vacancies than jobseekers, and inefficiently slack when there are more jobseekers than vacancies.

Finally, the section applies the formula to the US economy. In general the US economy is inefficient. It is especially inefficiently slack in slumps. For instance, the unemployment gap reached 6 percentage points during the Volcker Recession, the Great Recession, and the Coronavirus Recession. By contrast, in 2022, the US economy is inefficiently tight. The unemployment gap has been below -1 percentage point during the whole of 2022.

##### Lecture videos

- Introduction to social welfare and efficiency (notes )
- Introduction to the efficient unemployment rate (notes )
- Introduction to sufficient statistics (notes )
- A Beveridgean framework for welfare analysis (notes )
- Formula for efficient unemployment: $u^\ast = \sqrt{uv}$ (notes )
- Comparing unemployment and vacancies to assess efficiency (notes )
- Inefficiency of the US economy (notes )
- Efficient unemployment rate in the United States (notes )

##### Readings

- Michaillat, Saez (2022) – This paper derives the formula $u^\ast = \sqrt{uv}$. The formula is based on the assumptions that servicing a vacancy requires about one worker; home production by jobseekers is almost nonexistent; and the Beveridge curve is close to an hyperbola (so the unemployment rate is inversely related to the vacancy rate). These assumptions are realistic in the United States. The paper then applies the formula to the United States, 1930–2022.
- Michaillat, Saez (2021) – This paper derives a formula for the efficient unemployment rate that generalizes the formula $u^\ast = \sqrt{uv}$. The general formula involves three sufficient statistics: Beveridge elasticity, cost of unemployment, and cost of recruiting.
- Chetty (2009) – This survey describes the sufficient-statistic method for welfare and policy analysis.

## Optimal monetary policy over the business cycle

Since the US unemployment rate is always inefficiently high in slumps, and sometimes inefficiently low in booms, monetary policy has scope to stabilize the unemployment rate better.

This section describes optimal monetary policy over the business cycle. Monetary policy influences the aggregate demand curve, so it can be used to shrink the unemployment gap. The optimal monetary policy is to adjust interest rates to eliminate the unemployment gap entirely. So the central bank should lower rates in bad times, when unemployment is inefficiently high, and raise rates in good times, when unemployment is inefficiently low.

In fact, given such optimality criterion, we can develop a simple formula for optimal monetary policy. The formula relates the optimal interest rate to two sufficient statistics: the unemployment gap and the monetary multiplier (the effect of the federal funds rate on the unemployment rate). In the United States, the monetary multiplier is about 0.5. The formula then indicates that the Fed should raise the federal funds rate by 2 percentage point for any 1 percentage point of unemployment gap.

##### Lecture videos

- Divine Beveridge-Wicksell framework (notes )
- Sufficient-statistic formula for optimal monetary policy (notes )
- Estimates of the monetary multiplier (notes )
- Optimal response to unemployment fluctuations (notes )
- Evaluating the behavior of the Federal Reserve (notes )
- Monetary policy in the dynamic model (notes )
- Beveridge curve in the dynamic model (notes )
- Replacing monetary policy by a wealth tax at the ZLB (notes )

##### Readings

- Michaillat, Saez (2022, sections 5–6) – These sections obtain the sufficient-statistic formula for optimal monetary policy and apply it to the US economy.
- Bernanke, Blinder (1993) – This paper estimates the response of the federal funds rate to unemployment, and the effect of the federal funds rate on unemployment.
- Coibion (2012) – This paper blends the narrative and VAR approaches to estimate the monetary multiplier—the effect of an increase in the federal funds rate on the unemployment rate. It obtains a median estimate of 0.5, so increasing the federal funds rate by 1 percentage point generally raises the unemployment rate by 0.5 percentage point.

## Optimal government spending over the business cycle

Monetary policy should eliminate the unemployment gap, but this is not always possible. Once monetary policy reaches the zero lower bound, for instance, it becomes impotent, and it has to be supplemented by fiscal policy.

This section studies how government spending should be adjusted when unemployment is inefficient. It shows that that optimal government spending deviates from the Samuelson rule to reduce, but not eliminate, the unemployment gap. The amplitude of the deviation depends on three sufficient statistics: unemployment gap, fiscal multiplier, and elasticity of substitution between public and private goods. Since the unemployment gap is countercyclical, optimal government spending is also countercyclical. That is, the government should spend more in bad times and less in good times.

##### Lecture videos

- When should fiscal policy be used for stabilization? (notes )
- Beveridge-Samuelson framework (notes )
- Labor force with public and private employment (notes )
- Marginal rate of substitution between public and private goods (notes )
- Elasticity of substitution between public and private goods (notes )
- Unemployment multiplier (notes )
- Effects of government spending on welfare (notes )
- Optimal government spending (notes )
- Samuelson rule (notes )
- Stabilization term (notes )
- Optimal deviation from the Samuelson rule (notes )
- Sufficient-statistic formula for optimal stimulus spending (notes )
- Properties of optimal stimulus spending (notes )
- Stabilization achieved by optimal stimulus spending (notes )

##### Readings

- Michaillat, Saez (2019) – This paper studies optimal government spending in the presence of inefficient unemployment. It derives the sufficient-statistic formula for optimal stimulus spending.
- Samuelson (1954) – This paper studies optimal government spending in a neoclassical model and derives the famous Samuelson rule.
- Ramey (2013) – This paper uses structural VARs on US data to estimate the unemployment multiplier—the effect of an increase in government spending on the unemployment rate.