Macroeconomics for the 21st century: Part 1, Theory

Roger Farmer

What are the implications of combining Keynesian ideas with Walrasian general equilibrium theory in a way that does not assume sticky prices? This column presents the first of a two-part outline of a new macroeconomics paradigm for the 21st century, starting with the theory.

Modern Keynesians base their ideas on a version of Keynes’ General Theory that assumes that prices and or wages are “sticky” (Clarida et al 1999). In a pair of columns, I summarise results from a research agenda that reconciles Keynesian economics with Walrasian general equilibrium theory in a new way that does not assume “sticky prices”. This column concentrates on economic theory. The next column explains how my ideas are connected with previous attempts to reconcile these Keynesian and classical ideas, and it draws out the implications of my work for economic policy.

My research focuses on two key ideas from Keynesian economics and one from microeconomic theory. The important Keynesian contributions are that free market economies may support any unemployment rate as an equilibrium and that the equilibrium we observe is selected by confidence or in Keynes’ words “animal spirits”. The key idea from microeconomic theory is that individuals are rational and goal-oriented and they do not make systematic forecast errors. The theory that I will sketch out below is worked out fully in two working papers, (Farmer 2009a, 2009b) and in two books, (Farmer 2010a, 2010b) published by Oxford University Press.

Although I recognise that the market system may lead to inefficient outcomes with high unemployment, I do not believe that fiscal policy is the right response to a financial crisis. My reconciliation of Keynes with Walras is different from the orthodox approach, and it leads to a different policy proposal that I describe in more depth in Part 2 of this series.

Technical assumptions

The model I will describe is designed to capture two key ideas. First, any unemployment rate can be an equilibrium in the steady state. Second, the equilibrium that prevails is picked out by animal spirits in the asset markets. The simplest environment that captures my main idea has the following properties.

There are two distinct physical goods, capital and a consumption good. I need this assumption to ensure that there is a relative price of capital so that one can meaningfully discuss changes in asset prices.

Labour is traded in a market with costly search and recruiting. I need this assumption to ensure that unemployment persists in equilibrium.

There is a single unit of capital and a measure of labour of length one. Think of this as a large number of workers. The model will decide the fraction of them who remain unemployed.

Capital does not depreciate and cannot be reproduced. It is owned by firms and traded in a frictionless rental market.

The return to capital represents the profit stream of the firm. In the model, the price of a unit of capital and the price of a share in a company are the same. In practice, the relative price of capital and the value of the stock market are very different concepts. Complicating the model to allow for this distinction would not alter my main message although it is clearly important for empirical work.

There are two technologies. One is a standard neoclassical production function that explains how labour and capital are combined to produce a good. The other is a search technology similar to those that have been widely used in other search models of the labour market (see Pissarides 2000). The search technology produces filled vacancies from unemployed workers and corporate recruiters. These recruiters are employed workers. Instead of working as recruiters they could alternatively produce commodities.

I simplify the model by assuming that the entire labour force is fired at the end of every period and rehired at the beginning of the next period. This allows me to describe the equilibrium of the economy as a series of disconnected static problems.

In the real business cycle model that has dominated macroeconomics for twenty years, variations in employment occur because households choose to supply more or less hours to the market in response to variations in the wage over time. I assume instead that households do not value leisure and all of their members would like to find a job. Variations in employment, in my model, occur because of variations in the fraction of the labour force that are unemployed.

To close the model I assume in my working paper (2009a) that there is a single infinitely lived family that maximises the utility of its members. I show that this assumption implies that fiscal policy cannot be used to restore full employment.

In my other working paper (2009b), I relax the representative family assumption by allowing for a more realistic demographic structure with birth and death. I show there that fiscal policy can increase employment, but the fiscal multiplier is less than one and increased government purchases are predicted to decrease welfare.

The social optimum

Let’s suppose that households can appoint a social planner to organise production. This planner is charged with the task of maximising the welfare of the representative agent. How would she behave?

Since there is no feasible way to transfer resources from one period to the next, the planner faces a series of disconnected one-period problems. In each period she will maximise consumption by optimally allocating workers between two tasks. Some workers will be assigned to the direct production of commodities. Others will be assigned to the task of searching for new workers to hire. Since the activity of recruiting diverts resources from productive activity, the social planner will choose to leave some workers unemployed. The problem of the social planner is depicted in Figure 1.

The dashed curve represents the quantity of the consumption good that can be produced as the planner increases employment from 0 to 100% of the labour force by adding more workers to the recruiting department. Initially, adding more recruiters is productive and additional workers result in additional output. But once the planner reaches L*, additional employment becomes counterproductive. By employing additional workers, the social planner could achieve 100% employment. This is not a good thing to do since these workers would be so busy recruiting each other that no one would be available to produce goods. 1-L* is a good candidate for what Milton Friedman (1968) has called “the natural rate of unemployment”.

Figure 1. The problem of the social planner

What goes wrong in the labour market?

General equilibrium theorists have shown that under certain assumptions, free markets work well in the sense that a competitive equilibrium replicates the decisions that would be made by a benevolent social planner.

To decentralise a social-planning problem, general equilibrium theory posits the existence of a set of competitive headhunting firms that would operate the search technology. These firms would purchase, from households, the exclusive right to match an unemployed worker with a vacant job. They would purchase, from firms, the exclusive right to fill a job. Although we do see headhunting firms, in practice these firms act as substitute recruiting departments for firms that are too small or too specialised to run their own operations. They do not pay unemployed workers for the right to find them a job.

How would an organised employment market operate if it did exist? Suppose that a competitive headhunting firm were to offer to pay an unemployed worker for the right to match him with a job. A dishonest unemployed worker could turn down every job offer and continue to receive payments while remaining unemployed. Since there will often be good reasons to refuse a job, it would be impossible to write a contract in which the worker must take any job that he is offered.

A given number of jobs can be filled by a large number of unemployed workers and a few recruiters or by a few unemployed workers and a large number of recruiters. But should society match workers with jobs by asking a few unemployed workers to search for a lot of vacant positions or a lot or unemployed workers to search for a few vacant positions? I argue that either outcome can occur in the real world because the price signals that tell firms and workers how to behave are missing.

Search equilibrium

Search theory provides an alternative description of how the labour market works. Workers look for jobs, taking as given the probability that they will find one. Firms assign workers to the recruiting department, taking as given the number of workers that each recruiter can hire. Firms and workers take prices wages and rental rates as given as in Walrasian general equilibrium theory.

An equilibrium is a set of prices and a set of plans by firms and households such that firms maximise profit, households maximise utility, and demands and supplies are equated in all markets. The firing probability of a worker and the hiring effectiveness of a recruiter are determined by the fact that the number of workers who find jobs must be consistent with the aggregate search technology. These terms enter individual decision problems as externalities that appear, to the observer, to be productivity shocks.

The equilibrium concept I have described sounds a lot like the one used in search models that have been widely studied in the literature. See, for example, the survey by Richard Rogerson, Robert Shimer and Randall Wright (2005). But my concept has fewer equations than unknowns. Decentralisation of the social planning solution requires the addition of two markets and two prices: One for the time of a searching worker and one for the time of a searching recruiter. The search equilibrium adds just one price; the money wage.

As a consequence, my model has many labour market equilibria in the steady state. A given number of jobs may be filled by many searching unemployed workers and a few searching recruiters. Or it may be filled by a few searching recruiters and a large number of unemployed workers. The relative prices that should direct market participants to the optimal mix of unemployment and vacancies are missing.

I believe that search theorists have missed this fact because we are trained, beginning in graduate school, to look for a model in which prices and quantities are uniquely determined by fundamentals. When confronted by an underdetermined model, existing theorists have chosen to add an equation in an attempt to bring the theory into line with existing general equilibrium models. Typically they make the assumption, that when a firm and a worker meet, they bargain over the wage. I believe that a more fruitful theory can be developed by throwing away this assumption and recognising that there is a pervasive labour market failure, and as a consequence, any unemployment rate can be an equilibrium.

Conclusion

Although my theory of aggregate supply sounds superficially like the Hicks-Hansen description of Keynesian theory that was taught to generations of economists in the post-war period, it is very different. Unlike the Hicks-Hansen model, the equilibrium concept that I have described does not rest on some prices being away from their Walrasian levels and there are no forces in the model that cause some agents to want to charge different prices.

I have argued that it is time to drop the natural rate hypothesis and return to the Keynes of the General Theory. This is not just empty rhetoric. It has implications for the policies to be used to stabilise the real economy in the 21st century. I take up this theme in a companion piece, “Macroeconomic Policy for the 21st Century” (2010d).

This piece is part of a published article in the National Institute Economic Review (2010c). I thank the National Institute for permission to reprint it here. I also thank the National Science Foundation for their support of this research under grant SBR 0720839.

References

Clarida, Richard, Jordi Galí, and Mark Gertler (1999), “The Science of Monetary Policy: A New Keynesian Perspective”, Journal of Economic Literature, 37:1661-1707.

Farmer, Roger E A (2009a), “Confidence, Crashes and Animal Spirits”, NBER WP,14846.

Farmer, Roger E A (2009b), “Fiscal Policy Can Reduce Unemployment: But There is a Better Alternative”, CEPR Discussion paper 7526.

Farmer, Roger E A (2010a), Expectations Employment and Prices, Oxford University Press, Oxford, March.

Farmer, Roger E A (2010b), How the Economy Works: Confidence, Crashes and Self-Fulfilling Prophecies, Oxford University Press, Oxford, April.

Farmer, Roger E A (2010c), “Macroeconomics for the 21st Century: Full Employment as a Policy Goal", National Institute Economic Review, 211: R45-2R50, January.

Farmer, Roger E A (2010d), “Macroeconomics for the 21st Century: Part 2, Policy”, VoxEU.org, 28 February.

Friedman, Milton (1968), “The Role of Monetary Policy”, American Economic Review, 58:1-17.

Keynes, John Maynard (1936), The General Theory of Employment Interest and Money, MacMillan, London.

Pissarides, Christopher (2000), Equilibrium Unemployment Theory, The MIT Press, Cambridge, MA.

Rogerson, Richard, Robert Shimer, and Randall Wright (2005), "Search Theoretic Models of the Labor Market: A Survey", Journal of Economic Literature, 43:959-988.