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[Music] we shall commence this module by understanding permanent income hypothesis and the life cycle hypothesis according to permanent income hypothesis and the life cycle hypothesis the consumer is assumed to determine its level of consumption on basis of its income which it earns through its lifetime on a stable path but the alternative theories of consumption say that the optimal inter-temporal consumption behavior of consumers is actually restricted due to their ability to borrow to finance consumption chief modifications in this direction have been pioneered by the works of deaton and carol attah and carol 1996 this model takes into account the savings for precautionary motive or say as a buffer stock it is generally presumed that the precautionary or buffer stock savings arise mainly due to two assumptions held by deaton as well as carroll ditton 1991 assumes that the agent is always employed and hence has a positive income but carol assumes that the agent may face unemployment spell at some point in future and therefore will receive a zero labour income in that time period deton says that the savings act like a buffer stock protecting consumption against the bad draws of income when the consumers are not permitted to borrow the precautionary demand for savings interacts with borrowing constraints to provide a motive for holding assets hence this module is concerned with the optimal inter-temporal consumption behavior of consumers who are restricted in their ability to borrow to finance consumption after studying this module you shall be able to know about the flaws of permanent income hypothesis and the life cycle hypothesis understand the role of liquidity constraints behind the consumption behavior understand the idea of buffer stock savings examine the relationship between the accumulated wealth by the consumers and their level of consumption know about the empirical evidences on liquidity constraints and buffer stock savings models of consumption moving on to liquidity constraints the permanent income hypothesis assumes that the lending and the borrowing rates are the same for the consumers but we know that the consumers borrow at a higher rate than their savings on besides some individuals are unable to borrow more at any rate of interest these facts pose as a liquidity constraint on the consumers which influence their consumption decisions if they face high interest rates on borrowings they may choose not to borrow to smoothen their consumption when their current resources are low and if they do not borrow at all they have no choice but to have low consumption when their current resources are low the presence of liquidity constraints causes individuals to save as insurance against the effects of future falls in income the liquidity constraints also imply that the current income is more important determinant of consumption than predicted by the life cycle and permanent income hypothesis these theories actually fail to show that in reality when the permanent income is higher than the current income the consumers may be unable to borrow to consume at the higher levels in the expectation of higher income in future the liquidity constraints on the other hand can raise savings in two ways firstly if the liquidity constraints are binding the individuals will consume less and secondly even if the liquidity constraints are not currently binding but they may bind in future this will again reduce their current consumption the second case may happen if there is a chance of low income in the next time period it may force the consumer to consume less in the current period if there are liquidity constraints unless the individual has enough savings to compensate that fall in future income thus the presence of liquidity constraints forces individuals to save for precautionary motives in other words the savings are used as buffer stocks which are accumulated when times are good in order to maintain consumption when times are bad in simple words the liquidity constraint implies that consumption in any time period must be less than or equal to one or ct must be less than equal to y t thus under the borrowing constraint the consumer cannot borrow and has to make his consumption decisions on basis of their current income and the budget constraint this can be observed from this figure under the boring constraint we can see in the figure that apart from budget constraint the consumer faces the additional constraint that first period consumption cannot exceed first period income the shaded area represents the combinations of first period and second period consumption the consumer can choose thus the liquidity constraint affects the consumption decision but these decisions will be different in case of binding and non-binding constraints this can be observed from this figure the figure shows that there are two possibilities that the liquidity constraint can be binding or not binding in panel a the consumer wishes to consume less in period one then he earns so even if there is some liquidity constrained the consumer may continue with his or her existing level of consumption the borrowing constraint is not binding and therefore does not affect consumption in panel b the consumer would like to choose point d where the consumer likes to consume more in period one than he earns but the borrowing constraint prevents this outcome the best the consumer can do is to consume all of his first period income as shown by point e thus we can say that the existence of liquidity constraints leads us to conclude that there are two consumption functions for some consumers the borrowing constraint is not binding and consumption in both periods depends on the present value of lifetime income that is y1 plus y2 divided by 1 plus r here r is the discount rate of time for other consumers the liquidity constraint is binding the consumption function is c1 is equal to y1 and c2 is equal to y2 hence for those consumers who would like to borrow but are not able to do so the consumption decisions depend only on current income or in other words when the borrowing constraint is binding first period consumption equals first period income and the same is true for the second period d10 describes the consumption behavior of the consumer with liquidity constraint in three period model that is the end of period one period two and period three simply speaking consumers past present and future time periods hence there is a need of inter temporal utility maximization that is u is equal to e t submission of tau is equal to t up to infinity 1 plus delta t minus tau v into c tau where delta is greater than 0 is the time rate of discount and v c tau is the instantaneous utility function assumed to be increasing strictly concave and differentiable the evolution of assets is given by a t plus 1 is equal to 1 plus r 80 plus y t minus c t here a is for assets at any point of time y is the labor income c is the consumption and r is the real interest rate such that delta is greater than r the real interest rate is treated as fixed and known and all the uncertainty is focused on labour income yt labor is inelastically supplied and a t is greater than equal to zero and the marginal utility function lambda c t is equal to v dash c t is a positive monotone decreasing function considering the case of impatient consumers that is delta greater than r the cash in hand of the consumer at a point of time is x t is equal to a t plus y d that is x t is the maximum amount that a consumer can spend in period t x t is the maximum that can be spent on consumption in period t consumption in period t and t plus 1 must satisfy lambda ct is equal to maximum lambda xt beta et lambda ct plus 1. if the consumer is constrained consumption can be no higher than xt and the master utility no lower than lambda xt the constraint will bind if marginal utility at x t is higher than the discounted expected marginal utility next period otherwise the two marginal utilities are equated in the usual way from equation 2 and three x t plus one can be evolved as x t plus one is equal to one plus r into x t minus c t plus y t plus one in this constraint function the marginal utility today is equated to the maximum value of marginal utility in the constrained situation and that discounted expected value of tomorrow's marginal utility the marginal utility of money that is price of consumption p x t is equal to lambda f x t c t is equal to f x t is equal to lambda raised to power minus 1 into p x t imagining a series of time periods from 0 to n the marginal utility of money in initial period will be equal to lambda x because whatever x is it will be spent but in period one p one x is set by the borrowing constraint or to equate marginal utilities and also back in time without borrowing constraints it is the convexity of lambda x that controls a degree of precautionary saving with borrowing constraints the same role is played by px so the inherited convexity means that the same arguments for prudence and precautionary savings go through when borrowing is prohibited indeed px is more convex than lambda x the inability to borrow in adversity reinforces the precautionary motive the general properties of the solution are clear starting from some initial level of assets the household receives a draw of income if the total value of assets and income is below the critical level x star everything is spent and the household goes into the next period with no assets if the total is greater than x star something will be held over and the new positive level of assets will be carried forward to be added to the next period's income note that there is no presumption that savings will be exactly zero consumption is a function of x not of y and f x can be greater than less than or equal to y assets are not desired for their own sake but to buffer fluctuations in income when income is low there will be disc savings and when it is high there will be saving moving on to the empirical evidence of liquidity constraints there are many important works regarding the impact of liquidity constraints on consumers choices about consumption savings etc one such work is by japanese and pagano they investigated if cross-country differences in liquidity constraints are the main explanatory factors behind the cross-country differences in aggregate savings they try to capture the differences in conditions regarding taking loans down payments required to purchase restrictions on consumers credit bankruptcy and foreclosure laws etc then they tried to find if these differences are associated with differences in the saving rates they try to examine the relationship between loan to value ratio which is defined as 1 minus the required down payment for home purchases and the saving rate it was found that there exists a strong negative relationship between the two the regression equation result in this case pointed out that an increase of 10 percent in the required down payments is associated with the rise in the saving rate of 2 percent of nnp with these results they try to prove that similar results exist if we replace the loan to value ratio with availability of consumer credit thus the liquidity constraints have an important influence on aggregate savings the works of habad and judd tried to find the impact of liquidity constraints on consumption as well as the fiscal policy they emphasize that policy simulation models that ignore liquidity constraints result in flawed tax policy analysis they found that the existence of liquidity constraint is important in the determination of consumption behavior in a life cycle model forced lifetime saving due to liquidity constraint is substantial and if the inter temporal elasticity of substitution in consumption is small the incorporation of borrowing constraints enables the life cycle model to generate more realistic predictions about the size of the aggregate capital stock they argued that reduced capital income taxation financed by increased labor income taxation raises individual welfare depend on substantial interest sensitivity of saving in the life cycle framework and on the ability of consumers with low current earnings to borrow to finance higher labor income taxes with borrowing restrictions the gains from higher saving rates and output must be weighted against the efficiency losses from the reduced consumption of constrained individuals thus elimination of capital income taxation compensated by higher labor income taxation can reduce the welfare of a representative individual there are many other empirical studies like flavin 1981 and many subsequent authors which have found evidence that changes in consumption are positively related to predictable changes in income the microeconomic evidence primarily from the panel study of income dynamics that is psid is more mixed but hall and michigan 1982 and zelda's 1985 found a relationship between changes in food consumption and previously predictable income changes similarly bradford d long and lawrence summers note that from 1899 to 1916 essentially all consumption was done by liquidity constrained consumers further we discuss the buffer stock savings buffer stock saving behavior can emerge from the standard dynamic optimization framework when consumers facing important income uncertainty are both impatient in the sense that if income was certain they would like to borrow against future income to finance current consumption and prudent in miles kimball's sense that they have a precautionary saving motive the buffer stock behavior arises because impatience makes consumers want to spend down their assets while prudence makes them reluctant to draw down assets too far if wealth is below the target fear or prudence will dominate impatience and the consumer will try to save while if wealth is above the target impatience will be stronger and fear and consumers will plan to dissave in this context carol at all 1992 says that unemployment expectations are important in this model because when consumers become more pessimistic about their employment situation their uncertainty about future income increases so their target buffer stock increases and they increase their savings to build up wealth towards the new target while detail 1991 takes into account the liquidity constraint the model by carol at all says that if there is uncertainty about employment situation the consumer will try to maintain the buffer stock savings even if there is no liquidity constraint while deton did not treat unemployment in his model the simulation evidence presented in carroll's model suggests that unemployment expectations are probably a crucial factor in determining the amount and characteristics of buffer stock saving this model finds a high degree of uncertainty as the households may occasionally experience very bad outcomes in which their incomes drop essentially to zero even with unchanging expectations about the average future level of income changes in the expected probability of bad events that is spells of unemployment have a major impact on current consumption and saving interestingly while standard life cycle and permanent income models imply that the interest elasticity of saving should be strongly positive in the buffer stock model the interest elasticity of saving is approximately zero let us understand the basic model considering a standard inter-temporal consumption model that is maximize e t is equal to 0 to t beta t mu c t such that w t plus 1 is equal to r w t plus y l t minus c t where y lt is equal to p t v t and p t plus 1 is equal to g into p t into n t plus 1 here y lt is a total family non-capital income or sale labor income for short vt is the multiplicative transitory shock in the ert and pt is a permanent labor income in ert which can also be defined as the value of labor income if no transitory shocks occur that is vt is equal to 1 nd is period t is multiplicative shock to permanent labour income capital g is equal to 1 plus g where capital g is the growth factor and the small g is a growth rate w is net wealth capital r is equal to 1 plus small r where small r is the interest rate and capital r is the interest factor beta is equal to 1 upon 1 plus delta is the discount factor where delta is the discount rate and c is consumption the standard constant relative risk aversion or crra utility function is of the form uc which which is equal to i repeat which is equal to c 1 minus rho divided by 1 minus rho where rho is the coefficient of relative risk aversion in order to generate buffer stock saving behavior it is necessary that consumers be impatient in the sense that if they faced no income uncertainty they would want to borrow against their future income in order to consume more today since the consumer is assumed to be impatient the condition required to exhibit impatience is rho raised to power minus 1 multiplied with r minus delta which is less than g if income is perfectly certain the growth of consumption would be approximately equal to rho raised to power minus 1 multiplied with difference of r and delta if the consumer has no wealth at all the present discounted value or pdb of consumption will be equal to the pdv of income if the growth of consumption is less than the income at the same pdv the level of consumption must be higher than the level of income thus if income was certain and p raised to power minus 1 multiplied with r minus delta is less than g the consumer would wish to spend more than income thus the consumers are impatient in their initial life but as they grow older and g falls with age they will be no longer impatient but in reality we know that people always say for the rainy day this fact raises a question why does buffer stock behavior arises can all at all say that if shocks to consumption are log normally distributed using the euler equation the consumption will grow according to delta log ct plus 1 which is equivalent to rho raised to power minus 1 multiplied with r minus delta plus 1 upon 2 rho e t variance of delta log c t plus 1 plus e t plus 1 hence the variance in consumption that is e t variance delta log c t plus 1 is negatively related to wealth that is a consumer with less wealth have less ability to buffer consumption against income shocks thus they have higher variance and faster consumption growth the growth rate of consumption is high when wealth is small because the level of consumption is being depressed by precautionary saving therefore over time as precautionary saving adds to wealth consumption will become less depressed this relationship can also be understood with help of the following figure the figure shows the relationship between the gross wealth ratio expected consumption growth and income growth consumers are impatient as rho raised to power minus 1 r minus delta less than g the line with arrows traces out the relation between expected consumption growth that is e t delta log c t plus 1 in the next period and gross wealth in the current period that is x t as x t approaches its minimum possible level h underscore expected consumption growth approaches infinity where h underlined is meant to signify the negative of minimum possible present discounted value of future labour income this is because as gross wealth x t approaches etch underline ct must approach zero the expected level of ct plus one is positive even if the consumer enters period t plus one with no assets therefore as x t approaches h underline e t delta log ct plus 1 approaches infinity on the other hand as x t approaches infinity uncertainty about future labour income becomes essentially irrelevant to consumption thus as x t approaches infinity the consumption growth rate approaches the growth rate under certainty rho raised to power minus 1 r minus delta as everything in this model is assumed to be continuous and monotonic the expected consumption growth rate will cross the income growth rate curve at one point the gross wealth ratio at this point will be called x star or the target gross wealth ratio it is a target ratio in the sense that if actual gross wealth is below x star the consumer will spend an amount small enough so that gross wealth will be expected to increase however if actual gross wealth is greater than x star the consumer will spend enough so that expected gross wealth next period will decline as shown by arrows on the expected growth rate curve the modules result differ under alternative parameter values for instance increasing g the growth rate of future income will decrease the target wealth stock by shifting the intersection with the e t delta log ct plus 1 curve to the left thus higher future income results in higher current consumption hence lower saving and lower wealth increasing the discount rate will shift rho raised to power minus 1 r minus delta down therefore e t delta log c t plus one curve will also shift down decreasing target wealth increasing the interest rate will shift rho minus one r minus delta up pushing e t delta log c ct plus 1 up and increasing target width increasing the degree of uncertainty in income will increase the variance of consumption growth for any level of wealth directly shifting the et delta log ct plus 1 curve up and increasing target wealth increasing the coefficient of relative risk aversion rho will have two effects it will shift the e t delta log c t plus one curve up as row variance delta log c t plus 1 increases tending to increase wealth as a direct effect of increased risk aversion it will also shift the rho raise to power minus 1 r minus delta curve down thus tending to reduce wealth this is the effect of a lower inter temporal elasticity of substitution moving on to the buffer stock model and some empirical evidence there is sufficient empirical evidence to suggest that the keynesian and the standard permanent income hypothesis or pih and life cycle hypothesis or lch do not hold true in life and the consumers behave according to buffer stock model carol and summers in 1991 across the countries and within the same country over time the growth rate of consumption tends to be very close to the growth rate of income the mechanism for this is adjustment in the capital stock if consumption is too high and growing more slowly than income the capital stock will be declining as the capital stock declines the interest rate increases and as a result the growth rate of consumption tends towards a growth rate of income conversely if consumption is low and growing faster than income the capital stock will be increasing driving interest rates down and reducing the consumption growth rate hence the steady state is eventually achieved with consumption growth equal to income growth campbell 1987 also showed that the current savings are equal to the present discounted value of expected declines in income campbell and mencu in 1989 further provided evidence to prove that for both total consumption and consumption of non-durables and services spending responds significantly to predictable changes in income in this study the unemployment expectations variable has a negative coefficient implying that consumption growth is slower in periods when consumers are pessimistic about future unemployment conditions campbell and return 1989 and many others have found that consumption appears to exhibit excess smoothness with respect to changes in permanent income they emphasized that there is some sort of excess smoothness of consumption with respect to changes in unemployment expectations in this perspective ricardo caballero 1992 interprets it as a model of near rationality but it could just as easily be interpreted as one in which even non-durable consumption spending has fixed adjustment cost he finds that such a model can generate exact smoothness of consumption with respect to shocks to permanent income such a model would also generate excess smoothness with respect to changes in uncertainty thus providing at least a potential for joint explanation of both kinds of excess smoothness thus we can find many papers which provide macro evidence in sport of buffer stock saving model let us now summarize what we have learned in this module the permanent income hypothesis and the life cycle hypothesis the consumer is assumed to determine its level of consumption on basis of its income which it earns throughout its lifetime on a stable path but the alternative theories of consumption say that the optimal inter-temporal consumption behavior of consumers is actually restricted due to their ability to borrow to finance consumption these models such as the model based on liquidity constraint and the buffer stock saving take into account the savings for precautionary motive or say as a buffer stock the precautionary of the buffer stock savings arise mainly due to uncertainty about future income or the capacity to repay the borrowings in future time period the precautionary demand for savings interacts with borrowing constraints to provide a motive for holding assets hence for these consumers the current income and its growth is a stronger factor determining the current level of consumption and its growth then assumed by the pih and lch you