We do have a political system - seems to revolve around making sure rich people get richer and the financial and military sectors larger and larger. But an economic system is supposed to allocate resources. Formally from Wikipedia
An economic system is the structure of production, allocation of economic inputs, distribution of economic outputs, and consumption of goods and services in an economy. It is a set of institutions and their social relations.
For instance a pack of wolves has a clearly defined economic system revolving around the institution of marriage and the social relations of a hierarchical
nuclear family (1–2 adults, 3–6 juveniles and 1–3 yearlings). A Redwood grove has an economic system using the
institution of brotherhood and the social relations of pure competition.
Certainly Americans live in nuclear families. But do we have any definable resource allocating organization at a level higher than family?
Both wolves and Redwoods have a higher level resource allocation decision making process in sexual selection. Technology investment decisions made by competitive sexual selection (Redwoods use a combination of pollination and budding) can be powerful - for instance Redwoods use fire by producing fire resistant bark and having seeds set to germinate after high heat.
Traditional human economic systems were based on family then tribe then village then city-state and then nation. But these systems have the problem described in Guns, Germs and Steel of results being tied to war and geography. All outcomes are a result of the resources available - in the past these were farmable plants and animals and large areas in the same temperate zone. Today resources such as oil and rare earth elements are in conflict but resolution of these conflicts by traditional war is difficult when many nations have weapons of mass destruction. So globalism has so far removed nationalism as a reasonable economic system. That doesn't mean that nationalism could not or should not be revived again with another Cold War like system but currently it is not dominant enough to be considered the United States economic system.
At first glance the tremendous wealth inequality in the United States might seem to define an institution of resource allocation. But there are severe limits to the consumption available to even the wealthiest. For instance a wealthy person can afford to buy a Tesla Roadster but technology like solid-state batteries will not be available for at least six years. Had different economic decisions been taken those batteries and recharging stations would be available now. The rich person is likely not a factor in those decisions. Also a rich person cannot legally have a harem in this country and inheritance is taxed; further limiting families as an institution. Wealth inequality has an effect on population but with constant immigration it would be a stretch to say that American population levels are controlled by it.
Ignoring the wealth inequality one could argue that elections are the institutional heart of the American economy. The government does have a say in research and development of technology, immigration levels, and many other parts of the economy. However our current US government seems limited to simple reactions to problems like running out of oil or a financial crisis. How many houses will be built and who will own them? Now with even US states approaching bankruptcy it is hard to perceive an orderly government decision making process.
Corporations are another possible choice of main decision making economic institution. They have global reach and unprecedented ability to control elections. They conduct research, have a say in immigration levels, and purposely direct government policies. The problems with corporations as the unit of allocation decisions is that there is no equivalent of sexual selection to explain corporate corporate interaction. How does the FIRE (financial, insurance, real estate) sector get so large - where was that decision made? Financial lobbyists and former employees turned bureaucrat explains a lot but globalism and its flow of cheap goods, the subsequent decline of manufacturing and the rise of bankers cannot be explained simply as a decision made by a group of corporations. Asian nations were drivers of that change as well. Or the decisions that created the size of the entertainment industry. To some degree it was what the masses wanted but that would take us back down from the corporate level.
Can anything as coherent as what governs wolves and redwoods come from looking at a set of American or global institutions? The wolves and the redwoods are after all part of ecosystems. A wolf venturing beyond its pack to form a new one or a redwood outside its grove - they are at the mercy of resource allocation decisions of many different other species. We can imagine an ecosystem of American institutions competing for control but without some structure to the conflict its somewhat just another way of restating that there is no American economic system. If true then we are limited to recording outcomes without understanding underlying mechanisms. Like measuring the sizes of wolf packs and their overall health without ever understanding how they really function.
If an economic system is a set of institutions and their social relations and America has no coherent economic system then it should be no surprise if America does not have much coherent social relations either. Some Americans traditionally perhaps heavily used the institution of nationalism and its local equivalent. Or others came from very large families. Others worked for one corporation or in one union their entire lives and believed strongly in that entity. Or further back there was the institution of slavery. Many early Americans organized around the institution of religion. Many now participate in the institution of academia. In the past some of these institutions were strong enough to define decision making for a nation or part of a nation. And therefore also the associated social relations held more strongly as well.
As a professor of mine once put it, "We're all going to miss fighting communism." Whatever else happens in the Middle East it is clear that there is no substitute for the Cold War to be found there. If America wants an economic system its going to need to look inward. Meanwhile social relations and everyone's overall sense of purpose will suffer. The power vacuum will fill with squabbling would be alpha leaders and trees falling in the forest with no orderly succession of kin using the resource.
Per traditional marketing America's great weakness of not having an economic system is touted as its greatest strength. The rather doublespeak term "market economy" encompasses the idea that an economic system need not be guided by institutions or social relations at all
A market economy is an economy based on the power of division of labor in which the prices of goods and services are determined in a free price system set by supply and demand.
Obviously the free price of a cure for Athlete's foot cannot be set in a "market economy" if no such cure has been found yet. And the research necessary to find the cure is likely much broader than paying to study the one disease. Even if that research is conducted and a cure found the cost of that research cannot be paid by any single medicine. So the free price of the cure really has little to do with the cost of its invention or the cost of its manufacturing or the demand and more to do with some convoluted agreement involving government policy reached between all interested parties. In the wolves economic system the cost of a disease is calculated as a function of the effect it has on a diseased wolf's ability to sire offspring. In the economic system described in Guns, Germs and Steel societies that made decisions that gave them an advantage in war would prosper and so the cost of technology investment could also be set in terms of the advantage it confers. Mercifully for humans these kinds of economics systems are dieing - the less technologically advanced parts of the world are currently growing in population far faster than advanced countries.
The lack of a coherent economic system doesn't mean that powerful people can't occasionally make resource allocating decisions. Steve Jobs or someone in Apple decided to hire patent owner Tony Fadell and the result is the iPod. President Obama and others recently put pressure on the government owned GM that resulted in the introduction of the plug-in car, Volt, and probably influenced the concurrent release of electric vehicles like the Leaf. And the solid-state battery company in the article linked above was spun out of government research. Even in the absence of an economic system progress can be made in an ad hoc way - innovation from chaos. But that approach might only be sufficient for very simple or extremely threatening situations.
Genetically modified foods, non-oil transportation, stem cell applications, sustainably grown foods, sustainable energy, planned communities, sustainable manufacturing, robotics, types of education - the list of potential resource allocations that have been cast adrift by the lack of an American economic system are endless. Our daily lives are full of activities and environments that exist as a result of decisions that were never thought about by anyone, nor taken by any organized system, nor resulting from any process that can be explained. There are large planned communities in other countries with common schools, play areas, parks and rivers whose equivalent home cannot be bought in this country no matter how much money you have. No amount of wealth will keep you safe from pollution. The current focus on GDP and employment figures ignores the obvious - what was the money spent on and what are the employed doing?
At other times in human history it could be assumed that a society that was almost uniformly incorrectly allocating resources would eventually be wiped out. Now food and shelter can be produced in volumes that are difficult to grasp and so no such assumption can be made. If we want the sense of purpose that came before just by surviving and reproducing we need to adopt the sort of institutions known previously only to the world of art. The "market" will not guide us; the equivalent of art critiques, salons and very educated consumers are required. America has no economic system. What we have is enough noise and confusion that people forget what's missing and why we need it.