The going assumption of the mainstream economists is that all schools of economic thought require the usage of the IS-LM curve abstraction. Some call this the Keynesian cross. To set the record straight, Monetarists fall into this paradigm, they are considered New Keynesians.
Carl Menger, the founding economist of the Austrian School, arose during the Marginal Revolution as the creator of the Subjective Theory of Value. This unique and solely applicable approach of using ordinal value scales to elucidate the subjective valuation of individual actors, is strictly and only of the Austrian School of Economics.
Some supposed Austrians (GMU and other conventional academic institutions) attempt to amalgamate schools of thought or even distinct theories, with what is the pure Mises-Rothbard method. Certain economists lacking in the knowledge of free-market economics may, through misapprehension, label this as completely purist. Rothbardians take this as a necessary compliment.
As is commonly the case, schools of economics are associated with political parties. This is an entire misunderstanding of the purpose of economics in general. Because of this, Austrians are not politically affiliated. Economics is a theoretical system that assists people in better comprehending the world, as is the case with any other theory (Math theory, Physics theory, Science theory and so forth).
The world exists, and later theoreticians elucidate what they may perceive as having occurred (a priori) so that others can then garner the confidence necessary so as to make better choices. The positivists use historical data and observations (a posteriori) to attempt to contrive future predictions.
The latter method is constructed many times on mere presumption, and becomes deceptive as the supposed predictions believe historical scenarios will occur once again given certain factors. Statistics are then found through sortition and sample sizes, and the prediction is erected within a certain confidence interval.
As I reiterate the aforesaid from previous posts, it is important for us to decipher the nebulous aspects of mathematics, most specifically, in economics. Indeed math tools become the means by which we can gauge more precise ends, yet we must remember it is not always what many innumerates may consider it to be. Math, and other theories, are not absolutes, they are ideologies which synoptically conjecture what life's mysteries may contain. These mysteries are observed and thence axiomatic.
As these axioms became embraced by the erudites of the learned theories, people then moved away from the more traditional thoroughgoing value system. Some may hearken to natural law and natural rights--the Golden Rule and for others the Non-Aggression Principle. This transgression had dire consequences.
All other schools of thought, disregarding the Austrian School, most commonly revert to utilizing Keynesian models. Only the Austrian School adheres to the descriptive method of economics, while evading the desire to calculate an abstract equilibrium. Keynesianism is in essence, not a priori, but a posteriori.
Subjective Value Theory states that value derives from the individual mind, where one's actions evince their choice on their ordinal value scale, and thus the commencement of the structure of production is understood. Land then has value derived subjectively, as do all other goods and choices in the economy.
The Labor Theory of Value is negligent to this concept. They do not believe value is subjective, yet inherent. Value for them, is stated in the prices of which aggregates concoct through a supposed calculable equilibrium. Furthermore, the labor theory of value adherent believes labor diffuses value. The laborer cannot negotiate his price, only the fixed cost that the company sets is then the value inherent in the good.
The main difference between the schools of thought is the misapprehension, or one could even state, the complete lack of understanding on the rate of interest itself. Within the Austrian School, Bohm Bawerk's Capital Theory lays the foundation for the true nature of this mark-up, and consequently the importance of money and what inflation really is. Accordingly, the Real Business Cycle Theory is in no way a descriptor of how the business cycle occurs. Only the Austrian Business Cycle Theory can lay claim to this elucidation.
If one is to falsely suppose that inflation is found at the lowest order good stage of the structure of production, based upon an assumed average of a basket of randomly chosen goods, then indeed the failure lies there. Money through historical regression is a product of subjective value, and time preference (the mark-up or rate of interest), becomes ever the more enhanced with real savings.
Government, as the IS-LM curves attempt to justify, reduces real savings. The Keynesian rate of interest is unknown and as abstract as their theory of value is. For this reason they are a posteriori, as they desire quelling a supposedly disequilibrating animal spirits that if left untamed would result in massively tumultuous business cycles.
Austrians understand the quelling of the business cycle (booms and busts) is found within roundaboutness, by which factors are advanced voluntarily to each stage of the structure of production constantly and without end. Equilibrium is nonexistent, and without false price signals (with the existence of private money) then inflation is mitigated. Money is key, and as a consequence government created moral hazards should be nixed. Government should not exist.
Governments have no savings, and hence they pilfer once their money is introduced. They, ergo, expand credit to fund their wages and public goods. The overconsumption of savings arises, and in order to boost aggregate demand, call for the rapid abridging of real value. At this point in time the absence of real value (purchasing power) causes this to occur perpetually, as gold is money (of real value).
This rate of interest found within the preference of time of the individual is then distorted due to their desire for monopolization--savings (capital stock) and purchasing power are extorted. Austrians desire building an economy on savings, as one's choices would be much more wary and better calculated in absence of inflation.
Social Security tends to reduce the desire of individuals to save for the future. Inflation as well, by deceptively lowering the rate of interest (cheap credit money), then increments the quantity of jobs which are contingent upon a balance sheet engorged with overinflated assets and elevated equity prices, among other things.
If money were understood to the Keynesian, government would not exist. As the individual purveys to the market their preference for time (desire to withhold), then indeed it may seem quite obvious that money must also arise naturally on the free market from the preference of the individual. Fiat is now en vogue, as we have forgotten the true nature of money and have thus substituted it for the servility to nationhood.