2.1. The Direct Mechanism by Which Borrowing Affects Household Expenditure Structure
Based on the consumer intertemporal choice framework, Dynan [
18] proposes a precautionary savings model in which the variance of changes in consumption expenditure measures uncertainty in expenditures, thus examining precautionary savings. The model assumes that the utility function is additively separable over time, with
,
, and
, whereas labor income is uncertain. At period
, the dynamic optimization problem of consumption for a representative household can be expressed as:
In Equation (1), is the expectation based on the information set in period , denotes the length of the lifespan, and t + j represents a particular period within the lifespan. is the time preference rate (assumed to be a constant), and is the consumption of a given consumer in period t. In Equation (2), is the nonhuman wealth of a consumer in period , and is known. is the after-tax real interest rate; is labor income (which is uncertain). Additionally, the utility function is additive separable over time and concave, and labor income is assumed to be uncertain.
Using the Bellman equation of dynamic optimization to solve this consumption model yields the first-order condition in
:
Applying the second-order Taylor expansion to
gives:
Neglecting higher-order terms in the Taylor expansion and substituting Equation (4) into Equation (3) yields:
Let
be the coefficient of absolute risk aversion, and define −
as the coefficient of relative prudence. Equation (5) provides a method to estimate the intensity of precautionary savings using panel data on consumption. Suppose
is the growth of an individual’s consumption of period
,
is the total number of periods, and
and
represent error terms from replacing the sample mean with the expected value and from preference shocks influencing the marginal utility of consumption, respectively. Then:
Substituting Equation (6) into Equation (5) yields:
where consolidating the error terms gives:
Given the initial assumptions , , and , we can see theoretically that should be a positive value. According to Equation (5), consumers’ expected uncertainty about future expenditures is positively correlated with the current period’s savings rate. Equation (8) indicates that if consumers in period anticipate increased uncertainty in period , leading to higher expenditures in period , they will reduce current consumption (all else being equal) to increase precautionary savings in order to address future uncertainties. This means that when consumers expect tighter borrowing constraints in the next period, they anticipate more difficulty in obtaining loans in the future and thus undertake precautionary savings in response. Conversely, when consumers’ borrowing constraints are relaxed, precautionary savings decline, thereby boosting consumption.
Based on this theoretical reasoning, we propose the first research hypothesis:
H0: Borrowing has a positive effect on total household consumption.
2.2. Mechanism of the Indirect Influence of Borrowing on Household Expenditure Structure
Borrowing primarily affects low-income groups by relaxing borrowing constraints, making it easier for these groups to obtain financial support, and indirectly influencing their expenditure structures via intermediary effects. To more clearly illustrate the relationship between borrowing and income growth among low-income groups, Wang [
19] introduces a theoretical model that incorporates “financial exclusion of low-income groups” into the original theoretical framework. Meanwhile, it is assumed that households exhibit varying levels of production efficiency, some high, some low, leading to differences in the amount of capital obtained. Consequently, families with lower production efficiency also have lower income levels, thus placing them in a relatively disadvantaged position.
Suppose there are
households in an economy during period
. The
household possesses
units of capital, and the total capital stock can be written as:
At this point, the production function of the
household can be expressed as:
where
denotes the household’s production efficiency, which depends on factors such as the household’s overall educational attainment and the region’s level of economic development. When both
and
are natural numbers, the following conditions hold:
Let
be the production efficiency of
, the marginal production household. Households above
are considered high-income, while those below
are considered low-income. To maximize returns, a rational household prefers to select a capital usage
. Accordingly, its production behavior can be represented as:
In Equation (13), denotes the local market interest rate. Equation (14) specifies the borrowing constraint for the household, where denotes the “financial exclusion” factor and reflects the degree of financial exclusion in the given economy (). The larger the value of , the lower the degree of financial exclusion and, hence, the weaker the borrowing constraints on low-income groups, increasing the likelihood that low-income households can obtain credit. When , financial exclusion is severe, indicating high borrowing constraints on low-income groups, making it difficult for them to secure financing. Under this scenario, a single household can only rely on its initial capital to produce. When , the economy exhibits no financial exclusion; in other words, even low-income households face no credit constraints.
When the total capital utilized equals the total capital stock
, the financial market reaches equilibrium. If the equilibrium interest rate
equals the production efficiency
of the marginal production household
, the above equilibrium can be achieved. The total capital usage consists of the capital used by the marginal production household
plus the maximum amount used by the high-income households. Under these conditions, the equilibrium can be expressed as:
and given
, the financial market equilibrium condition is:
As financial exclusion gradually eases, low-income families can obtain financial services on an equal footing. In other words, as
increases, high-production-efficiency/high-income households will not fully use the maximum capital they could borrow; the remaining capital can be used by households with lower production efficiency. Consequently, some lower-efficiency, lower-income families will continuously replace the previously identified marginal production household
, becoming the new marginal production households. The total output at this point can be written as:
Because
, for all rural households
, then we have:
Equation (18) indicates that as financial exclusion declines, households with lower production efficiency and lower income can acquire more capital through financial channels to increase their incomes. The prerequisite is that the production efficiency exceeds the cost of using financial capital, .
From the above theoretical model, we conclude that borrowing aimed at low-income groups can influence household expenditure structures by raising their income levels.
Based on this theoretical reasoning, we propose the following hypotheses:
H1-1: Borrowing exerts a more pronounced positive effect on total consumption among low-income households and in areas that have recently overcome poverty; conversely, the effect is less pronounced among higher-income households and non-poverty regions.
H1-2: Borrowing positively promotes educational/training expenditures for low-income households and in formerly impoverished areas; conversely, the effect is less pronounced in higher-income households and non-poverty regions.
H1-3: Borrowing positively promotes agricultural production expenditures among low-income households and in formerly impoverished areas; conversely, the effect is less pronounced for higher-income households and non-poverty regions.
2.3. Mechanisms Underlying the Differential Impact of Borrowing on Household Expenditure Structures Across Varying Levels of Relative Poverty
Credit constraints affect household expenditure structures not through a single channel but via two distinct pathways: a direct effect and an indirect effect. Because different types of consumption items exhibit varying sensitivities to external factors, the composition of consumption expenditures changes accordingly. From the perspective of a rational household, consumption behavior aims to maximize utility by choosing the kinds and quantities of goods and services, subject to the household’s income and current prices.
For ease of derivation, Li et al. [
20] assume households make rational consumption choices and categorize household consumption into essential consumption and non-essential consumption, denoted by
and
, respectively. When the quantity of
has not reached a level satisfying basic needs, its marginal utility (
) is significantly larger than that of
(
). Hence,
where
,
and
,
represent the consumption quantities and prices of the two types of goods, respectively, and
is the budget constraint. In Equation (20),
denotes the household utility function. Defining the Lagrangian function:
where
is the Lagrange multiplier. By the Lagrange theorem, the optimal conditions
must satisfy the following three first-order conditions:
Dividing Equation (22) by Equation (23) yields:
Equation (25) indicates that household utility is maximized when the marginal rate of substitution between the two types of goods equals their price ratio. Let
be the quantity of essential consumption that meets the household’s basic needs. When
, the two sides of Equation (25) become:
where (27) indicates real number
that grows without bounds. Under such circumstances, Equation (25) does not hold. To maximize utility, the household allocates its entire budget
to purchasing
,
. Once
, the marginal utility of essential goods
begins to fall below a certain fixed value:
where
is a fixed constant. At this point, the condition for Equation (25) to hold is satisfied. To achieve maximum utility, the household’s consumption of
becomes:
From this theoretical derivation, when a household’s budget constraint is tight, the household must first meet its basic survival needs, leaving little for other goods. As the budget constraint loosens, once essential consumption is no longer the sole priority, the household will increase spending on non-essential items.
Based on the above theory, we propose the following research hypotheses:
H2-1: Borrowing has a positive effect on health-related (medical) consumption for low-income households and in formerly impoverished areas.
H2-2: Borrowing has a positive effect on “enjoyment-oriented” consumption for low-income households and in formerly impoverished areas.