Origins and Early Development of the Nonlinear Endogenous Mathematical Theory of the Business Cycle: Part I - The Setting

We study the emergence of the nonlinear, endogenous, theory of the business cycle, in mathematical modes, within the framework of a macroeconomic theory, which was itself going through its own formal 'birth pangs' at the same time, in the same years. The first part of the story begins in 1928 and ends, with the publication of Yasui's classic on Kaldor, Hicks and Goodwin, in 1953, and Hudson's classic of 1957. But there were other classics in the 1930s, even within some theories of the business cycles of the time - particularly the Austrian and that which may now be called the 'time-to-build' tradition, which originates in Marx and Aftalion, independently, and reaches its nonlinear formalization origins in Tinbergenís work of 1931, followed by Kalecki's theories of the business cycle, substantially influenced also by Tinbergen's classic for mathematical method. There is also what may, for want of a better name, be called the 'cobweb' tradition, on the one hand, and the tradition of Swedish Sequence Analysis, on the other (especially in the 1937 classic work of Lundberg, summarising the Swedish discussion on business cycle theory). The former having its origins, partly, in Austrian inspired search for an integration of dynamic method with equilibrium economic theory (especially represented by a series of classics by Rosenstein-Rodan, from about 1929); and partly in the well known phenomenon of lagged responses in the supply-demand interactions in agricultural and commodity markets, particularly elegantly formalised by Leontief in 1934. From the point of view of economic theory, they were all part of the emerging consensus on the need to incorporate money and áuctuations in nontrivial ways as intrinsic components of orthodox equilibrium economic theory which was characterised as static theory. The implication was that the search was for a synthesis of dynamic method with traditional static equilibrium economic theory. The origins of macroeconomic theory, generally attributed to the post-depression development of monetary theory, business cycle theory and the theory of policy, could be traced to this particular search for a synthesis and was brilliantly summarised by Kuznets in a series of pioneering contributions in 1929/30. The story we try to tell is of mathematical business cycle theory in its non-linear modes, and how it emerged from one strand of macroeconomic theory, which, as just mentioned, was itself being forged, ab initio, dynamically

The net worth trap: Investment and output dynamics in the presence of financing constraints

This paper investigates investment and output dynamics in a simple continuous time setting, showing that financing constraints substantially alter the relationship between net worth and the decisions of an optimizing firm. In the absence of financing constraints, net worth is irrelevant (the 1958 Modigliani–Miller irrelevance proposition applies). When incorporating financing constraints, a decline in net worth leads to the firm reducing investment and also output (when this reduces risk exposure). This negative relationship between net worth and investment has already been examined in the literature. The contribution here is providing new intuitive insights: (i) showing how large and long lasting the resulting non-linearity of firm behaviour can be, even with linear production and preferences; and (ii) highlighting the economic mechanisms involved—the emergence of shadow prices creating both corporate prudential saving and induced risk aversion. The emergence of such pronounced non-linearity, even with linear production and preference functions, suggests that financing constraints can have a major impact on investment and output; and this should be allowed for in empirical modelling of economic and financial crises (for example, the great depression of the 1930s, the global financial crisis of 2007–2008 and the crash following the Covid-19 pandemic of 2020).</jats:p

Origins and Early Development of the Nonlinear Endogenous Mathematical Theory of the Business Cycle

We study the origins of the nonlinear, endogenous, theory of the business cycle, in mathematical modes, within the framework of a macroeconomic theory, which was itself going through its own formal "birth pangs" at the same time, in the same years. The first part of the story begins in 1928 and ends, with the publication of Yasui's classic on Kaldor, Hicks and Goodwin, in 1953, and Hudson's classic of 1957. But there were other classics in the 1930s, even within some theories of the business cycles of the time - particularly the Austrian and that which may now be called the "time-to-build" tradition, which originates in Marx and Aftalion, independently, and reaches its nonlinear formalization origins in Tinbergen's work of 1931, followed by Kalecki's theories of the business cycle, substantially influenced also by Tinbergen's classic for mathematical method. There is also what may, for want of a better name, be called the "cobweb" tradition, on the one hand, and the tradition of Swedish Sequence Analysis, on the other (especially in the 1937 classic work of Lundberg, summarising the Swedish discussion on business cycle theory). The former having its origins, partly, in Austrian inspired search for an integration of dynamic method with equilibrium economic theory (especially represented by a series of classics by Rosenstein Rodan, from about 1929); and partly in the well known phenomenon of lagged responses in the supplydemand interactions in agricultural and commodity markets, particularly elegantly formalised by Leontief in 1934. From the point of view of economic theory, they were all part of the emerging consensus on the need to incorporate money and fluctuations in non-trivial ways as intrinsic components of orthodox equilibrium economic theory which was characterised as static theory. The implication was that the search was for a synthesis of dynamic method with traditional static equilibrium economic theory. The origins of macroeconomic theory, generally attributed to the post-depression development of monetary theory, business cycle theory and the theory of policy, could be traced to this particular search for a synthesis and was brilliantly summarised by Kuznets in a series of pioneering contributions in 1929-30. The story we try to tell is of mathematical business cycle theory in its non-linear modes, and how it emerged from one strand of macroeconomic theory, which, as just mentioned, was itself being forged, ab initio, dynamically

Quantitative Methods for Economics and Finance

This book is a collection of papers for the Special Issue “Quantitative Methods for Economics and Finance” of the journal Mathematics. This Special Issue reflects on the latest developments in different fields of economics and finance where mathematics plays a significant role. The book gathers 19 papers on topics such as volatility clusters and volatility dynamic, forecasting, stocks, indexes, cryptocurrencies and commodities, trade agreements, the relationship between volume and price, trading strategies, efficiency, regression, utility models, fraud prediction, or intertemporal choice