Hall's Random Walk Hypothesis

I derive the key result known as Hall's Random Walk Hypothesis. This says that, using some simplifying assumptions, the best estimate of consumption tomorrow is the value of consumption today.
This result builds on results found in previous videos. Primarily this is the stochastic Euler equation. We assume a quadratic utility function and make a simplifying assumption about the consumer discount rate. we then derive a result regarding certainty equivalence.
In previous videos, I derive the intertemporal budget constraint for a two-period model of intertemporal choice. I shall derive this for more periods. Check out the playlist for intertemporal macroeconomics as a whole, linked at the end of this video.
We discuss the assumptions of the two-period model of intertemporal choice. This involves consumers living for 2 periods. They can consume, save or borrow in these time periods, allowing for consumption that differs from their income in that period. In order to defer income to other periods, they can buy or sell one-period bonds with interest r.
We can then mathematically write the budget constraint for each of these periods. With a bit of substitution and rearranging, this gives us the intertemporal budget constraint. This says that the present value of consumption is equal to the present value of income. The consumer can thus not spend more than she earns, but will spend all of her income since more consumption is always assumed to increase her utility.
In future videos I shall consider the intertemporal choice between labour and leisure that an optimising consumer must make.
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[@muneemhussain4582]

Excellent video. You are very good at explaining things. Keep it up :D

[@EverythingEcon]

Thank you!

[@ChristopherAhenkan]

Using the random walk model, discuss with necessary derivations that changes in consumption is unpredictable

[@ChristopherAhenkan]

Using the random walk model, discuss with necessary derivations that changes in consumption is unpredictable

[@mphileconscovid4133]

why did u differentiate the left side thus the aCt-bCt

[@EverythingEcon]

I'm not sure I fully understand the question, but the stochastic Euler equation has the derivative of utility on the left hand side. Our simplifiying assumption gives us a formula for utility. We thus have to differentiate this before substituting it in