I'm a newbie in the Austrian School of thinking.
I'm reached the chapter in my non-Austrian required textbook dealing with economic principles. The book, which hasn't taken any stance but just presents the readers with various theories, says that one cause of inflation could be unemployment. That is, high inflation is caused by/correlated to low unemployment rates, and low inflation correlates with high unemployment rates.
What should we make of this theory?
It is just an observed phenomenon that periods of high inflation correlate with higher employment. The reason that this occurs is that it only looks at the short term. Inflation in the short term raises demand, but that demand falls once the bills inevitably lose value. In the long run, the inflation makes things worse because it distorts the structure of production in that those who are the first recipients of the new bills get the bills at the old value and as the bills pass from person to person they decrease in value until eventually they reach their new, diminished value. Companies will have relatively grown and shrunk due not to consumer demand but rather political favoritism.
So don't worry about the Philip's Curve. Empiricism is a faulty school of thinking for many logical reasons.
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The Philips curve is an empirical observation that correlated inflation rates with employment rates (noticed a direct relationship). Keynesians took this information and (a) used it as empirical proof of their theories (namely that there's a direct relationship between aggregate demand, employment, and prices), and (b) made all sort of prescriptive interventionist policy recommendations for various governments and administrations (an inflation-employment trade-off that central planners can directly manipulate in order to stimulate economic growth).
In the short-run this relationship does exist, but only because inflation lowers wages in real terms which increases the QD for labor (laborers are the last to receive the newly created sums of money, and therefore their incomes are the last to rise, and will rise by a relatively smaller degree). In the long-run, however, this empirical relationship breaks down (as Hayek, Mises, and Friedman predicted) as prices adjust. Additionally, the stimulative effects of monetary injections suffer from diminishing returns. In other words, a progressive and continuous expansion in the supply of money is required in order to produce the same stimulative effects.
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When was your textbook written? 1965? No-one uses the Philips Curve these days (at least not without caveats).
It's also correct to say that it is not a causal 'theory', just a correlation.