Baby Sitting Coop

Monetary Paradoxes of Baby Sitting Cooperatives

Now submitted to Journal of Post Keynesian Economics, see comment below

New Title and Writeup emphasized the contributions and radical implications of the model. Previous title was: SUNSPOT EQUILIBRIA OF BABY SITTING COOPERATIVES.

INTRODUCTION

Classical economic theory of the time could not explain the Great Depression, nor the prolonged high unemployment which followed. Keynes argued that this was the result of insufficient aggregate demand, which could be fixed by expansionary monetary policy. These ideas became widely accepted, and constituted the basis for monetary policy until the 1970’s. Keynesian theories conflict with the neutrality of money, and suggest that expansion of money leads to inflation only under full employment. Keynesian theories gradually fell out of favor following stagflation resulting from oil price shock in the 70’s. This led to emergence of alternative macroeconomic theories, as well as a search for micro-foundations for Keynesian economics. This paper provides some micro-foundations for certain Keynesian phenomena in a specialized economy. The model providing surprising insights into the nature of these phenomena.

The Global Financial Crisis of 2007 has led to a renewed interest in Keynesian theories. In particular, Krugman in “The Return of Depression Economics” argued that Keynesian ideas remain relevant to understanding contemporary recessions. To motivate this, he has used a real world example of the Capitol Hill Baby-Sitting Cooperative (BSC). According to an analysis by economists who were members of the Cooperative, the BSC suffered from a recession due to a shortage of “scrip”, the currency used to exchange baby-sitting services.

Krugman’s analysis is based on an intuitive and heuristic analysis by Sweeney and Sweeney (1977). However, the BSC is a very simple single good economy, where the sole function of money is to allow for inter-temporal trade. This simplicity allows for a rigorous analytic treatment. Our research was motivated by the idea of analytically validating the intuitive insights of the Sweeneys and Krugman. Is the BSC a Keynesian economy? Can a shortfall of money create a recession in this economy? A simple model which displays Keynesian effects should be useful in building understanding of these phenomenon in more complex situations. Previous analyses of the BSC have come to the following conclusions.

1. In a purely heuristic analysis, Sweeney and Sweeney (1971) argued that the BSC is a Keynesian economy – insufficient money leads to recession, while excess leads to inflation. Krugman uses the Sweeney arguments without further analysis.

2. With motivation similar to ours, Hens et. al. create a mathematical model for the BSC economy. They show that the BSC economy displays Keynesian properties. There is an optimum quantity of money, and too little money leads to recession. They also conduct an experiment which validates their theory, in that the experimental results conform to the theoretical predictions. They suggest that the existence of the optimum quantity of money is due to fixed prices – one unit of scrip can be exchanged only for one unit of baby-sitting.

3. With a somewhat different model and motives, the analytical analysis of Kash et. al. reaches similar results for the BSC economy. They find that increased money supply leads to increased exchange up to a critical limit which is the optimal quantity of money. They find a new phenomenon of a “crash”. Increasing money supply beyond the optimal quantity leads to zero trade as the value of money collapses to zero. Kash et. al. also suggest that the optimal quantity is due to fixed price of scrip.

All authors mention as significant the “fixed price” feature of the BSC economy. But in presence of fixed prices, the existence of an optimal quantity of money, and recession for low money is a triviality. The Keynesian rejection of neutrality of money is not based solely on sticky prices. In this paper, we create a simple model of the BSC economy to investigate the presence of Keynesian phenomena. The model leads to strange and paradoxical results, not available in earlier analyses. We list these results below.

1. The BSC Economy has the Keynesian Beauty Contest property. That is, equilibria depend heavily on the beliefs of agents about how other agents will behave. For the sake of definiteness, let us call this “second order expectation”: agents’ expectations about the decision making procedures being followed by other agents. Different types of 2^nd order expectations are possible, and lead to different types of phenomenon. All of the expectation mechanisms explored are “rational” in the sense of being self-fulfilling, creating a justification for believing in their validity.

2. The central question being investigated is: is money neutral in the BSC economy? This has a subtle, complex and perhaps paradoxical answer. In all models, money is “technically” neutral – that is, all levels of money are compatible with the same sets of equilibria. This is true even though prices are fixed. At the same time, money is not “expectationally” neutral. At any given level of money stock, coherent expectations about the value of money will be self-fulfilling. In our model, there are three possible coherent and self-fulfilling expectations about money: money is of high value, low value, or zero value. The quantity of money will fail to be neutral if changes in the stock of money affect the expectations about the value of money. If expectations are not affected, then changes in quantity of money have no effect on the equilibria and money is neutral in short and long run.

3. A paradoxical violation of Say’s Law: The BSC economy display several other phenomena which run counter to standard intuitions. Supply creates its own demand in two strong senses. In a single period, supply of baby-sitting is jointly produced with demand, and hence supply creates demand. In addition, all agents balance budgets across time, so that for any single agent, an act of supply is exactly matched by a demand for baby-sitting services at some other point of time. Despite this dual guaranteed match between supply and demand, some equilibria have excess supply, others have excess demand, and none have a match between supply and demand.

4. Breakdown of Partial Equilibrium Supply and Demand Analysis. This phenomenon of mismatch between supply and demand has been noted by many authors, and attributed to the fixity of price – one scrip is worth one half-hour of babysitting. We show that flexible prices cannot resolve this problem. One might expect that the partial equilibrium (PE) Marshallian theory would work in a single good economy. However, we will see that supply and demand cannot be separated as required by PE analysis, and thus the intuitions generated by supply and demand analysis do not hold up.

5. Excessive Trading is Possible. Intuition suggests that trade by mutual consent is always welfare improving, since both parties agree to the trade only under this circumstance. Thus, Kash et. al. argue that the volume of trade is a good indicator of welfare in the BSC economy. In our model, despite mutual consent, trades can be welfare decreasing, and banning certain trades can lead to welfare improvements. Equilibria with lower total trading volume can be superior to situations with higher trading volumes.

All of these paradoxical properties suggest that the surface simplicity of the BSC Economy is deceptive, and hides deep and murky complexities. Although it would be premature to jump to policy implications on the basis of such a simple model, these implications are valid for the BSC economy itself, and are radically different from those suggested by standard economic intuitions. Two of these implications are highlighted below:

1. The value of money can change from high to low and to zero depending purely upon expectations in the BSC economy. It seems likely that this phenomenon will generalize far beyond the simple BSC economy, since multiple equilibria driven by expectations are ubiquitous in monetary models; see for example Evans and McGough (2005). Central Bank responses to speculative attacks on currencies are guided by the intuition that the value of currencies are determined by fundamentals. Thus, speculators cannot win if the fundamentals are sound. Many Central Banks have bet heavily and lost heavily against speculators on the basis of these intuitions. In the BSC economy, the value of money does not depend upon fundamentals, but purely on expectations about the value of money. Thus a speculative attack can succeed just by changing expectations, without any change in the fundamentals. A subtle and complex interaction between fundamentals and the value of money occurs because of the nature of expectations. If everyone believes that fundamentals are relevant to the value of money, then this becomes a self-fulfilling prophecy. Speculative attacks will then take the shape of news about change in fundamentals, regardless of whether or not such change has occurred or whether the changes being described in the news actually matter in the determination of the value of the currency. As long as the news convinces the public, and changes their expectations about the value, the attack will succeed, regardless of Central Bank interventions. This matches empirically the way speculative attacks are conducted and has radical implications for policy in face of such attacks.

2. The Sweeneys and Krugman suggests that low money supply leads to a recession in the BSC economy. In our model, this can happen but has radically different implications from the ones drawn by these authors. First, the expansion of money works through the expectations effect, and so monetary problems are not purely technical. They have a social dimension and work through consensus about the value of money. Second, even though increased money supply may increase the volume of trade, this may actually decrease social welfare. Thus, the so-called recession state, with low volume of trade and high value of money, may actually be superior in terms of welfare to a high volume of trade with low value of money. Again this is in strong conflict with standard economic intuitions.

An important lesson from our model is that choice of a particular equilibrium among a multiplicity of Nash Equilibria requires agents to coordinate plans. The central message of Bicchieri (1997) is that we must go beyond individual rationality, and study how agents actually learn to resolve the coordination problem. Since this is exactly the forte of behavioral economics, the problem has been studied in different contexts in many experimental studies. Duffy (2008) has provided an extensive survey of this literature.

Submission History

OLD Abstract: Krugman has popularized the experiences of the Capitol Hill Baby-sitting Cooperative (BSC) as a fundamental paradigm for macroeconomic policy. Many authors who have formally analyzed the story have concluded that money must be supplied in an optimal quantity for smooth functioning of the BSC economy. We create a natural model of the BSC which has sunspot equilibria. Agents must co-ordinate their expectations to arrive at an equilibrium. Our analysis shows that many of the lessons derived from the experience of the BSC depend on a particular choice of the equilibrium. Other choices can be more efficient and lead to different lessons. In particular, money holdings act like sunspots; they matter only if all agents agree that they matter. Surprisingly, flexible prices cannot solve the problem of mismatch between supply and demand. Also equilibria with excess supply may be more efficient than outcomes where supply and demand are matched. Our model shows that there are deep lessons to be learned from the BSC economy, but they are of a rather different nature from those derived by most authors. How expectations are formed, and how agents learn about other agents strategies form a crucial part of the equilibrium. These must be part of good models, and suitable interventions must take these into account. How agents can consciously choose among multiple equilibria and learn to coordinate on a particular choice requires more attention from economists.

Keywords: Monetary policy, recession, Keynesian economics, sunspot equilibria

JEL Codes: D71, E52