{"id":196,"date":"2021-10-16T00:50:29","date_gmt":"2021-10-16T00:50:29","guid":{"rendered":"https:\/\/www.economic-instability.com\/?p=196"},"modified":"2024-06-07T11:57:28","modified_gmt":"2024-06-07T11:57:28","slug":"priming-the-pump-on-some-lessons-learned-from-samulesons-1939-accelerator-multiplier-model","status":"publish","type":"post","link":"https:\/\/www.economic-instability.com\/?p=196","title":{"rendered":"Priming the pump: on some lessons learned from Samuelson\u2019s 1939 accelerator-multiplier model\u00a0"},"content":{"rendered":"
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Cartoon published in the Trenton Evening Times, Oct. 15, 1937 which highlights Franklin Delano Roosevelt (F.D.R.) manoeuvring the pump with the help of Congress bringing water in a kettle labeled \u201cspecial session.\u201d Failing to pass labor legislation in 1937 at the occasion of that session, F.D.R. was compelled to restore public balance and implement contractionary fiscal policies. The cartoon is drawn from a post by Ben Zimmer on the site Language and politics (https:\/\/languagelog.ldc.upenn.edu\/nll\/?p=32649<\/a>).<\/figcaption><\/figure>\n

The Great Depression led to a profound renewal of how problems of governmental fiscal policy were tackled. With reference to the notion of the multiplier introduced by John Bates Clark, Richard Kahn and John Maynard Keynes, the idea that public expenditures could be used to pull the economy out of its slump gained more acceptance in the 1930s. In a series of articles published in 1939 and 1940, Paul Samuelson, then aged 25, urged his contemporaries to examine that idea on the basis of a macro-dynamic model. <\/span><\/p>\n

Inspired by Hansen\u2019s works, in particular his interpretation of the 1937 crisis (collected in his 1938 <\/span>Full Recovery or Stagnation?<\/span><\/i>) which was discussed during his seminar at Harvard, Samuelson crafted a model to highlight how a temporary change in public expenditures could leave the final position of the economy unchanged but influenced its trajectory. <\/span><\/p>\n

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Samuelson viewed his model as an introduction to Tinbergen\u2019s macro-dynamic works (see our other posts on this subject here<\/a> and there<\/a>); in this perspective, Samuelson was the direct heir of the macro-dynamic approach of cycles developed during the 1930s by Frisch, Tinbergen and Kalecki. Like them, he started from economic assumptions which he found in the work of \u201cliterary\u201d economists, in his case Hansen, Harrod, Keynes, Kahn, or Clark, and he developed from those ideas a closed model made up of three simple equations, whose combinations was nevertheless able to give rise to various dynamic trajectories.<\/span><\/p>\n

By analyzing these different trajectories, and what determined them, Samuelson was able to show how different economic policies would impact the final position of the economy and its trajectory toward it. The recession experienced by the US in 1937 was the case that he wanted to illustrate, to show when and how pump priming could lift the economy, but the determinants of the models clearly showed that expansions resulting from a temporary rise in public expenditures would always come at the price of severe recessions. Placed in the context of the 1937 crisis, when a contraction in public expenditures coincided with a sharp recession at a time when the economy had not completely recovered from the 1929-1933 depression, Samuelson\u2019s model turned out to be a clear and sharp warning on the necessity to consider the dynamics of the economy.<\/span><\/p>\n

Assuming that a macroeconomic equilibrium is reached at every point in time so that whatever is produced is entirely sold, Samuelson introduced the following equation: <\/span><\/p>\n

  <\/span>   <\/span>\"\begin{equation*}<\/p>\n

where \"Y_t\"<\/span> is global output, \"C_t\"<\/span> is the part of output sold to consumers (consumption), <\/span>I<\/span>t<\/span> is the part sold to firms (investment) and \"g_t\"<\/span> is the part sold to the government (public expenditures).<\/span><\/p>\n

To determine what drives \"Y_t\"<\/span> Samuelson introduced two behavioral equations accounting for the changes in \"C_t\"<\/span> and \"I_t\"<\/span>, which are two of the components in global demand or global spending. In accordance with Hansen\u2019s reading of Keynes, consumption is assumed to result from income generated one period earlier:<\/span><\/p>\n

  <\/span>   <\/span>\"\begin{equation*}<\/p>\n

where \"\alpha\" <\/span> is the marginal propensity to consume, that is, a coefficient telling how much any additional dollar received in \"t-1\"<\/span> is spent in \"t\".<\/span><\/p>\n

On the other hand, investment itself depends on changes in consumption. The decisions of firms to invest, or spend, depend on their ability to sell goods to consumers, and they base their decisions on the changes in consumption rather than its current level: they decide to spend more on investment when consumption is increasing and less when it is decreasing:<\/span><\/p>\n

  <\/span>   <\/span>\"\begin{equation*}<\/p>\n

where \"\beta\" <\/span> is the value of the \u201crelation,\u201d that is, a coefficient representing how much investment changes when consumption changes between \"t-1\"<\/span> and \"t\"<\/span>.<\/span><\/p>\n

In the end, the combination of these two hypotheses showed that income in time <\/span>t<\/span> depends on income in \"t-1\"<\/span> and in \"t-2\"<\/span>  :<\/span><\/p>\n

  <\/span>   <\/span>\"\begin{equation*}<\/p>\n

This shows that income in the present period depends positively on the previous period and negatively on what happened two periods before. Now, asked Samuelson, what would happen if the government decided to implement a temporary increase in public expenditures? What would happen if the pump was turned on and then stopped? The following application reproduces the trajectory of income in Samuelson’s model for temporary and permanent increases in public expenditures. The model starts in the equilibrium determined by \"Y_t = C_t + I_t\", and at time \"t=2\" a shock can be added, either permanently or only temporarily; different trajectories will result from different combinations of the parameters \"\alpha\" and \"\beta\". <\/span><\/p>\n