Overdeterminacy and endogenous cycles: Trygve Haavelmo's business cycle model∗ Andr´eK. Anundsen Tord S. H. Kroghy Ragnar Nymoen Jon Vislie June 7, 2011 Abstract Unlike Trygve Haavelmo's seminal contributions to econometrics, his research program in macroeconomic theory is not widely known. In this paper we present his short-run macro model for an economy with deregulated financial markets and a policy determined interest rate path. Driven by a mismatch between the marginal return to capital and the rate of return required by capital owners, a Wicksellian heritage, Haavelmo's model generates cycles. This highlights how today's stan- dard equilibrium models may have left out an important characteristic of how the economy functions. It further implies that care should be taken when conducting monetary policy. Adopting a strict nominal anchor as the main objective of mone- tary policy might generate disequilibrium, or imbalances, in the capital market. Keywords: investments, business cycles, monetary policy. JEL classification: E22, E32, E44, E52 The importance of the interest rate for continued economic expansion is not deter- mined by whether it is high or low, whether it is adjusted upwards or downwards etc, the whole point is to keep the inequality in favor of the marginal productivity of capital. Haavelmo, 1969, p.153, the authors' translation. ∗We are indebted to Olav Bjerkholt, Sheetal K. Chand, Eilev S. Jansen, and Asbjørn Rødseth for valuable comments. Krogh is grateful for funding provided by the Norwegian Research Council, project number 195135. yAll authors are affiliated with the Department of Economics, University of Oslo. Anundsen and Krogh are research fellows. Nymoen and Vislie are professors. Corresponding author: Tord Krogh, Postboks 1095 Blindern, N-0317 Oslo, [email protected]. 1 1 Introduction During the past twenty years, monetary policy has become much more central for macroe- conomic stabilisation policy than it used to be in the first decades after World War II. For example, a number of countries have imposed inflation targeting where the central bank (CB) publishes projected interest rate paths that are consistent with the inflation forecast reaching the target in a future period. The interest rate, and more specifically the interest rate path, is the policy instrument. During the same period, the models that are used to aid monetary policy have developed to become dynamic stochastic general equilibrium (DSGE) models.1 As the name suggests, these models are genuine equilibrium models, and despite short-run frictions, the economy is never far away from equilibrium over the policy horizon. Because of the inherent dynamic stability of the standard models they are not well calibrated to real world disequilibrium dynamics, recently exemplified by the Great Recession of 2007-2009.2 This observation indicates that there may be deeper forces set in motion by interest rate setting policies than smooth adjustment of prices, and that the potential of disequilibrium deserves more attention than hitherto in \the science of monetary policy".3 In the history of economics, many leading economists have analysed the potential and limitations of monetary policy in their work. John M. Keynes' "General Theory" is perhaps the most important single work. In this paper, we want to bring attention to a theory developed by the Norwegian economist Trygve Haavelmo (1911-1999). Not only was he a pioneer in the development of econometrics, for which he was awarded the Nobel Memorial Prize in Economic Sciences in 1989, but he made important contributions to macroeconomics, monetary theory and business cycle theory under influence of Frisch, Keynes and, not least, Wicksell. A recurrent theme in Haavelmo's theoretical contri- butions was the interaction between financial markets, capital markets, and the rest of the real economy, and that the 'likely' outcome of this interaction may be disequilibrium rather than equilibrium dynamics. Haavelmo wrote at the high tide of Keynesian fiscal policy activism and he lived in a country known for economic planning and regulated markets where sudden falls in the activity level, unemployment, and other business cycle phenomena were thought to be plagues of the past. Given this, it may seem surprising to claim that Haavelmo wrote anything of interest for today's economists. The solution to this paradox is that Haavelmo studied the role of monetary policy in models where markets were assumed to be completely liberalised and where firms and households in important respects behaved in accordance with the classical theoretical paradigm. Thus, Haavelmo formulated theo- ries that may have seemed far-fetched and of little relevance for the practically oriented economists of his day. The course of history has changed this and Haavelmo's macroeco- nomic theory now represents a perspective that seems surprisingly fresh and with many useful insights. Haavelmo's understanding of the linkages between the real economy and the finan- cial markets was inspired by the writings of Wicksell (1898, 1906), and his analysis of monetary theory can be seen as complementary to the arguments of Wicksell that led 1A standard reference is Smets and Wouters (2003). 2For recent critique of such models, see e.g. De Grauwe (2010a). 3This label is from Clarida et al. (1999). 2 to his famous cumulative process. This is concisely presented in Chapter 33 of the book \A Study in the Theory of Investment"(Haavelmo, 1960). There he outlines how a fun- damental overdeterminacy arises in standard models if the authorities choose to use the rate of interest as a policy instrument. This overdeterminacy is due to the properties of standard arbitrage conditions for the agents' portfolio decisions. Equilibrium in the financial market gives a relationship between the equilibrium real interest rate and the rate of return on capital. Since the rate of return is determined by the real economy, an exogenously set interest rate will make the model logically inconsistent (overdetermined). Macroeconomic equilibrium, both in the classical and modern sense, is based on a model which is logically consistent, so when overdeterminancy occurs one of the main premises for smooth equilibriating dynamics is lost. In this situation, one important task for macroeconomic theorising is to present models of how the economy realistically func- tions when the equilibrium model no longer applies. Below, we explain how Haavelmo took up the challenge, and how he arrived at a model with non-linear dynamics and endogenous cycles. These model properties are interesting in themselves, and they mark a stark contrast to the predictions of the modern DSGE models used to guide monetary policy. As noted, Haavelmo had studied Wicksell and he pointed out that adding a dy- namic element in the form of a cumulative inflation process is another way to make the model consistent.4 However, in Haavelmo's own short-run macro model it is the quanti- tative variables ('the level of economic activity') that bears the bulk of the disequilibrium dynamics. This means that there is a definitive Keynesian flavour to Haavelmo's model. In addition to his 1960-book, the best source to Haavelmo's macroeconomic model is perhaps \Orientering i makro-økonomisk teori"(\A Study in Macroeconomic Theory "), Haavelmo (1969), henceforth referred to as SMT. A main topic of the book is how to design a logical system for understanding and managing a complex decentralised market economy, consisting of agents pursuing individual, and often conflicting, goals. This book was on the reading list for several generations of Norwegian economists, but was never completed as a textbook in English. Moene and Rødseth (1991) provide an excellent presentation of Haavelmo's contribu- tions to econometrics and economics.5 Our paper supplements theirs by focusing on the aspects of Haavelmo's theories that are relevant for monetary policy and for understand- ing the business cycle.6 Unlike Wicksell's cumulative process, Haavelmo's contribution to macroeconomics is largely unknown among contemporary economists. This also holds for his interpretation of the cumulative process as a force potentially created by the fun- damental overdeterminacy. Hence our goal is to make some of his ideas better known to a broader audience. The rest of the paper is organised as follows: We start out in Section 2 by presenting Haavelmo's law of indifference in the capital markets. In Section 3 it is shown how this implies a fundamental overdeterminacy in a macroeconomic model where the monetary authority sets the interest rate. Disequilibrium will be an intrinsic feature of such mod- 4Haavelmo stressed that the model would then be unable to reach a stable stationary equilibrium. 5Morgan (1990) is the first academic appraisal of Haavelmo's Probability Approach to Econometrics, see Bjerkholt (2005, 2007) for a recent contribution. The reader is referred to Nerlove (1990) for a more critical appreciation of Haavelmo. 6Andvig (1993) also discusses some of these issues. Further, in an article written in Norwegian, B˚ardsenand Nymoen (2001) make use Haavelmo's conceptual framework to aid the interpretation of their macroeconometric model of inflation targeting. 3 els, and we explain how Haavelmo translated the overdeterminacy into dynamic forces by utilising the desire to purchase new or get rid of existing capital equipment. His endoge- nous regime-switching business cycle model is explained in Section 4, whereas the scope of his ideas today are discussed in Section 5. Section 6 concludes. 2 The Law of Indifference in the Capital Market A line of thought characterising many of Haavelmo's writings is what impact an unregu- lated capital market will have on the economy, and the implications for private investment activity. Like in other Western economies, the Norwegian capital market remained heav- ily regulated for a long period of time after the Second World War.7 Even long before full deregulation had taken place, Haavelmo outlined a monetary theory and its policy implications within a deregulated and decentralised context.