5 c y a a 1 t 1 t 1 t t a r y c t t t δ α since a t

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(5) C - Y + A = A 1 - t 1 - t 1 - t t A r) - ( + Y = C t t t δ α
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Since A t = (Y-C) t-1 , from the budget constraint, we can write the first differenced version of the LCH as Hence wealth appears implicitly in this ECM-type specification. Note however that there is considerable uncertainty over (a) what measure of wealth might affect consumption behaviour (b) whether the level of wealth is important, or whether what matters is changes in the level of wealth, particularly perceived changes in wealth due to changes in the price level. Much recent work on the consumption function has been concerned with investigating the role that wealth (or some subset of it such as liquid assets, housing wealth etc) plays in practice in influencing consumption behaviour. Some models have included interest rates as a regressor (to proxy one component of the return on wealth, or prices (to proxy for perceived wealth revaluations, or for price mistake effects-see below). (5) However, despite consumer expenditure and income variables being measured in real terms, DHSY do also find a role for inflation effects in the determination of non-durable consumers expenditure. Their equation (45) is: DHSY do not provide an explicit account of the role played by prices, but note that it is consistent with Deaton's argument that consumers (temporarily) mistake changes in the average price level for changes in relative prices.
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