He held positions as a professor of Mathematics and Psychiatry at The George Washington University, where he established leading academic programs directed to solve real world problems. Minsky has made many contributions to AI, cognitive psychology, mathematics, computational linguistics, robotics, and optics.

Consumers become more reluctant to part with dollars, as they have been made worse off in the future and prefer to save. Unfortunately, after this steepening, the expenditure supply curve now intersects with the sticky-prices region of the expenditure demand curve.

What kind of interventions might we try to fix this? Conventionally, our first resort is to discourage financial saving and promote current expenditures by reducing interest rates: We have entered the liquidity trap, if you believe in such a thing. But we are certainly not out of potential of interventions.

Suppose we believe that the central bank is very, very good at setting expectations. Then… fig 7 That worked! Yay monetary policy, still potent at the zero bound! But, we should be careful. Plus, perhaps engineering an uptick in inflation expectations is hazardous.

Perhaps the central bank cannot set expectations precisely, so that there is a hazard of overshooting and generating inflation rather than just restoring equilibrium. My two period setup is pretty Ricardian. Encouraging private spending through a taxes and transfers deficit in Period 1 only works if that deficit is not repaid by running a surplus in Period 2.

In this case, debt effectively repays itself over time, without ever requiring surpluses. If you think transfers that will never be paid for in taxes must increase the expected future price level, then in the immediate term, all that does is to reduce the scale of the program necessary to eliminate the output gap!

An increase future price level expectations, like the unfinanced transfer itself, renders the expenditure supply curve shallower, helping carry our equilibrium out of the recession region.

But this is not realistic: We do not have to restrict ourselves to taxes and transfers, but can have government deficit-spend on real goods and services directly. And when we tax-and-transfer, we can also redistribute. But I have played with variations in which government spends, rather than transfers its deficit, and with redistribution.

But is that a realistic assumption?

However, governments do sometimes respond to recessions by adopting stimulus programs, which in rough approximation we can model very easily. So the expenditure supply curve due to stimulus is vertical. Including expenditure due to government stimulus simply shifts the expenditure supply curve to the right by the quantity of nominal dollars appropriated!

For ordinary consumers, the quantity of expenditure supplied always goes to zero as the price of a dollar in terms of goods and services falls to zero. The curve bottoms out at the origin of the graph.

With stimulus via direct spending, the government commits to current-period expenditure regardless of the price level. The expenditure supply curve now bottoms out to the right of the origin. That is, our model suggests that it might be possible for a government to balance its budget in the teeth of a recession and still stimulate its way out of the recession!

Our balanced budget is stimulative if and only if spending is increased and balance is accomplished by increasing current taxes. Cutting spending to balance the budget would be contractionary under our framework, while increasing taxes to fund spending is expansionary. The intuition is pretty straightforward:Alexey Radul's 13 research works with 36 citations and reads, including: Probabilistic programming with programmable inference.

Alexey Radul has expertise in Medicine and Mathematics. In mathematics and computer algebra, automatic differentiation (AD), also called algorithmic differentiation or computational differentiation, is a set of techniques to numerically evaluate the derivative of a function specified by a computer program.

AD exploits the fact that every computer program, no matter how complicated, executes a sequence of elementary arithmetic operations (addition. [4] Alexey Radul, “Propagation Networks: A Flexible and Expressive Substrate for Computation”, PhD Thesis, MIT, My thesis committee, Guy Steele Jr., Patrick Winston, and Tom Knight, has also been invaluable.

I am particularly indebted to Guy for his meticulous and insightful comments as my dissertation neared completion. Not only graduate school but life in general would have been completely dif-ferent without Gregory Marton's unfailing friendship. Alexey Radul Thesis Opinion essay sample topics free stem cell research papers essays physical and chemical hooks for essays about school uniforms essay satire examples.

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As an undergraduate, I worked on projects in parallel processing, digital systems, signal processing, mobile applications, and probability. As a master’s student, I worked on dynamic system-level binary translation for x86 virtualization.

Several of my projects resulted in papers presented at workshops.

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Alexey Radul - ICFP