Financial Inclusion, Financial Depth, and Macroeconomic Fluctuations

3.1.1 Household Sector

There are two types of households. First, there are households that maximize their lifetime utility under an intertemporal budget constraint, known as Ricardian or intertemporally optimizing households. Due to their access to capital markets, these households are able to save or borrow money. The latter group, known as rule-of-thumb or non-Ricardian households or financially excluded, uses up all of their current labor income and is unable to access capital markets. Presumably, θ ∈ [ 0 , 1 ] households are of the first type, and 1 − θ households are of the second group. The second level of classification divides θ into savers, θ S , and borrowers, θ B , households. These households differ with respect to their discount factors only, that is, β t s > β t B .

Within Ricardian group R = {S, B}, both representative households maximize expected lifetime utility considering a CRRA utility function with distinct consumption preferences ( C t R = { C t s , C t b } ) and working hours ( N t R = N t s , N t b ) .^[1] Utility is based on the deviation of consumption of household C t R from lagged consumption, C t − 1 R . The model features internal habit persistence, and the degree of habit formation is denoted by h . The disutility from labor is parameterized by θ N . R . It is the inverse of Frisch labor supply elasticity.

The savers’ households allocate income from the labor market ( W t ) and return from the deposit I t − 1 d D t − 1 s on current consumption and new deposit holdings. Borrowers’ households allocate income from the labor market and loans on current consumption and for the payment of previous loans. As in Iacoviello (2005), the borrowing capacity of households is limited by collateral constraints. Macro-prudential authority confines the borrowers’ access to loans to a fixed proportion of their wage income by imposing an LTI ratio.

A combination of intra-temporal trade-offs between working hours and consumption, as well as intertemporal substitution in consumption, results in aggregate consumption that revolves around real interest rates ( r t − π t + 1 ) , past ( C t − 1 ) , and future consumption ( C t + 1 ) . The degree to which consumption reacts to an interest rate is determined by the intertemporal elasticity of substitution θ c and habit persistence ( h ) , which is the deposit rate r t d a n d r t h for savers and borrowers’ households, respectively. The following is the consumption Euler equation for saver households:

For borrowers’ households, the Euler equation takes the following form:

The log linearized form of borrowers’ borrowing constraint is given as follows:

where ϑ h , t is the (stochastic) LTI ratio. With such a constraint, any idiosyncratic shock to borrowers’ wage income limits the optimal leverage of borrowers.

Following Gerali et al. (2010), ϑ h , t presumably follow the stochastic AR(1) process

where η t ϑ is an i.i.d. shock to the LTI ratio and ϑ h ¯ is the steady-state LTI ratio for households borrowing.

The consumption of financially excluded households is given as follows:

For intermediate good producers, households provide differentiated labor and while, wages are set in a staggered pattern with a constant Calvo probability ( 1 − ξ w ) of renegotiation in each period. However, remaining households optimize by setting a wage μ t w mark-up relative to the MRS between consumption and leisure mrs t . It can be written as

The remaining households’ wages are partially indexed using ι w as a parameter for inflation. The following wage equation is the outcome of partial indexation plus non-reoptimized wages:

In addition to wage mark-up and a cost-push shock to wages ϵ t w , equation (7) demonstrates that real wage is a weighted average of past and expected future wages as well as past, current, and expected inflation rates. The difference between actual wages and wages that would have prevailed in a fully flexible labor market is ϕ w , while the indexation of non-reoptimized wages ι w establishes the strength of the association between current wages and past and current inflation.

3.1.2 The Production Sector

The production sector is made up of perfectly competitive final goods producers who combine the intermediate goods to create homogenous final goods and monopolistically competitive firms that produce intermediate goods. Aggregate output y t is subject to fixed cost ϕ p augmentation using Cobb–Douglas technology and exogenous level of technology ϵ t a

where α captures the share of capital in production. The capital utilization rate z t and the capital stock is aggregated to make capital service k t s and represented in the equation below:

Furthermore, the optimal capital utilization rate is obtained by equating the cost of increased capital utilization with the capital service rental price

The marginal product of capital is denoted as mpk t in the context of the cost-minimization problem. The elasticity of utilization cost with respect to capital inputs is represented by ψ

The following is the marginal product of labor that also arises from the firm’s cost minimization problem:

Monopolistically competitive firms likewise follow staggered contracts in price settings similar to wages. Following Calvo setting, a number of firms are able to revise their prices using constant Calvo probability ( 1 − ξ p ) , and they are able to set prices at a mark-up μ t p over wages. Prices that are not optimized have a partial index ι p to past inflation. As a result, the following process is assumed by inflation π t dynamics:

Equation (13) represents a hybrid NK price Philips curve, where the backward-looking portion results from partial indexation, and the forward-looking behavior is represented by the expected future inflation term π t + 1 . Additionally, the evolution of the current inflation process is determined by a price mark-up shock ϵ t p .

3.1.3 Investment and Entrepreneurs

In order to derive the Euler equation for investment, one must assume that new capital stock K t is produced by capital producers in a competitive market to rent out to firms or producers of intermediate goods at a fixed rental rate of r k . The capital producer must either invest in additional capital I t or alter the utilization rate z t of already installed capital in order to determine the supply of capital rental services K t s . The costs associated with both actions for a capital goods producer are quadratic capital adjustment cost φ . Below is the investment equation

Comparable to consumption, the value of installed capital q t and the weighted average of the past i t − 1 and future investments i t + 1 make up the current investment i t . Capital adjustment costs also lead to shock to the investment, which reduces investment temporarily. Investment shock ϵ t i is an exogenous AR(1) process.

Given the log-linearized standard capital accumulation equation

The current value of installed capital q t is expressed as a positive function of its own expected future value, the expected future marginal product of capital mpk t + 1 and a negative function of the ex-ante real interest rate ( r t − π t + 1 ) , in the corresponding arbitrage condition

where r k ¯ is the steady-state rate of return on capital and δ is the rate of depreciation. The shock for the rate of return on equity investment is denoted by ϵ t q .

Entrepreneurs maximize utility from consumption and finance by renting capital to intermediate goods producers and borrowing from banks. The key factor depicting the level of FD arises with the assumption that entrepreneurs need collateral to take loans. The following is the Euler equation for entrepreneurial consumption:

Entrepreneurial loans are subject to the following collateral constraints:

where the maximum permissible leverage ratio is determined by the LTV ratio, represented by ϑ e . Like ϑ h , t , ϑ e , t is also a stochastic AR(1) process. Since both households and entrepreneurs consume, aggregate consumption is the sum of their consumption expenditures.

3.1.4 Banking Sector

The structure of the banking industry complies with Gerali et al. (2010). The banking industry is made up of a range of commercial banks that compete monopolistically. Two monopolistically competitive retail branches – the loan and deposit branches – and one perfectly competitive wholesale branch, make up each Bank (j). The deposit branch collects deposits from households and deposits them at the wholesale branch. Because the wholesale deposit rate r t d , is driven by arbitrage in the interbank market, the wholesale branch pays the retail deposit at the policy rate r t . Receiving loans from the wholesale branch, the retail loan branch pays the wholesale branch at r t l . The maximization problem of the wholesale branch for loans and deposits against constraint where loans advanced are tied to deposits D _t bank capital K t B . Bank issues loans to households and entrepreneurs, which are financed by deposit D _t bank capital, K t B . The maximization problem of the wholesale branch gives rise to the following equation for interest rate spread:

The bank capital evolves as follows:

The retail loan branch collects loans from the wholesale branch and advances them to borrowers’ households and entrepreneurs at differentiated rates, r t h , r t e , respectively. The maximization problem of the retail branch gives rise to the following interest rate evolution for both households and entrepreneurs:

where z = {borrower households, entrepreneurs}. The equation illustrates how the loan rate setting is influenced by the stochastic mark-up, past and expected loan rates, the wholesale loan rate, and the marginal cost of the loan branch determined by the policy rate and the bank’s balance sheet position. ϵ t z is bank mark-up shock and follows the AR(1) scheme.

3.1.5 Aggregation

Because of the resource constraint, the aggregate output is divided into four categories: government spending, investment goods, consumption, and resources lost due to variable capital utilization

where the steady-state percentages of GDP for household consumption, investment, and capital utilization loss are c y , i y , and z y , respectively. The shock to government spending ϵ t g is defined as ϵ t g = ρ ϵ g ⁎ ϵ t − 1 g + ε t g , in which ε t g ∼ i . i . d . N ( 0 , σ ε g 2 ) and ρ ϵ g denote the auto-covariance coefficient in the exogenous AR(1) process that characterizes the shock.

4.1.1 Cost-Push Shock

Figure 5 shows the response of key macroeconomic aggregates on an adverse cost-push shock (depicted in equation (12)) for low, medium, and high levels of FD without considering financial exclusion. Cost-push shock is contractionary for output. Although aggregate consumption, working hours, and loans advanced also reduce; nonetheless, at disaggregated levels, dynamics vary across savers and borrowers and households and entrepreneurs. Savers’ households pay the cost of shock in terms of foregone consumption, whereas both entrepreneurs’ and borrowers’ households are better off in terms of consumption. This may be attributed to the decrease in interest rates for both households and entrepreneurs on their loans. A decrease in interest rate induces entrepreneurs’ loans to increase leading to a higher level of investment. Moreover, the passing-on of an increase in cost to prices is also indicated in a higher level of inflation in response to shock. This induces the policy rate to increase in impact, and its effectiveness in controlling inflation is ubiquitous in the longer term.

Figure 5

Cost-push shock for varying degrees of financial depth (left) and access (right).

It is evident from the figure that the effect of cost-push shock on macroeconomic aggregate is efficiently mitigated in the environment with higher and medium levels of financial depth. A low level of financial depth enhances the cyclicality of macroeconomic aggregates substantially. This implies that a well-developed financial system insures entrepreneurs against cost-push shock and results in the level of economic contractions far below than in a system with inadequate financial depth. This conforms to the findings of Beck et al. (2002), who deliberate that the development of financial intermediaries enhances the macroeconomic volatility in the face of real shock.

Figure 5 also presents the MF arising in response to an adverse cost-push shock in an economy with three levels of financial inclusion and a medium level of financial depth. In a model for different levels of financial inclusion, a positive cost-push shock generates an impact contraction for the output and consumption for 9 quarters, while employment contractions persist for 17 quarters. The response to inflation and interest rate is positive, while in the long run, a decline is observed before returning to the equilibrium level. Financial inclusion of different extents attenuates the negative impact of shock for output, employment, and wages, while for inflation and interest rate, negligible impact differences are found in responses. Low financial inclusion makes the shock persist for longer.

The shock propagates similarly to the above case, where full inclusion is considered with different levels of financial depth. However, contrary to the above case, where a lack of financial depth magnifies the adversity of shock, higher financial inclusion magnifies fluctuations in output and aggregate working hours, while for the rest of variables, high exclusion is observed to magnify the impact of shock, particularly for loans advanced. The findings reveal that FD, through the increase in financial inclusion, mitigates the contraction arising from cost-push shock. Moreover, the general overview of results indicates high inclusion as a favorable policy option for FD instead of full inclusion.

4.1.2 Productivity Shock

The production function presented in equation (7) specifies the productivity shock. Macroeconomic expansion follows in response to a positive productivity shock, as presented in Figure 6. Overall, the responses of key macroeconomic variables are consistent with previous research. The easing of policy interest rate and its effectiveness in reducing inflation in the face of productivity shock is ubiquitous in the current model. Neither the magnitude nor the persistence of productivity shock is responsive to the level of financial depth except for policy rate and savers’ consumption. Our results for consumption conform to Bhattacharya and Patnaik (2016) report that consumption is more volatile when financial inclusion increases.

Figure 6

Productivity shock for varying degrees of financial depth (left) and access (right).

The bearing of productivity shock for business cycle fluctuations is not independent of the different levels of financial inclusion. Output and aggregate consumption increase remarkably higher for full inclusion cases as compared to cases where the financial market is segmented. For monetary and financial variables, low inclusion is magnifying and causing the effect of shock to persist. It is also observed that the positive impact of favorable productivity shock on output and consumption is highest in the full inclusion case, but the impact persists longer for the high inclusion case. This indicates that though productivity shock propagates to key aggregates similarly for all three cases of financial inclusion, nonetheless, amplification and persistence of shock vary to different extents.

4.1.3 Monetary Policy

The responses of the main macroeconomic variables to the unanticipated monetary policy shock shown in the Taylor rule are plotted in Figure 7. Real economic variables decline in response to a contractionary monetary policy shock, with a peak response occurring in the fourth quarter. The strength of the monetary transmission mechanism and the average lag time of the economy’s reaction to monetary policy actions are both supported by the conventional evidence in these responses. Amplification and persistence of monetary shock are evident for low levels of FD.

Figure 7

Monetary policy for varying degrees of financial depth (left) and access (right).

On impact, the response of macroeconomic variables to monetary contraction is not substantially different for the three levels of financial inclusion. The amplification and persistence of monetary contraction over an extended horizon varies moderately with the change in financial inclusion. Particularly for real variables persistence is high for high inclusion. Interest rate inertia, which is observed for all three cases, is substantial for low inclusion cases. Consequently, more contractions are faced by the economy characterized by highly financially inactive households in the face of monetary policy shock.

4.1.4 LTI and LTV Shock

The favorable shock to LTI ratio on households’ borrowings, as specified in equations (3) and (4), induces households to borrow more and increase their consumption. Loans to entrepreneurs are crowded out and cannot get momentum even with remarkable monetary easing. Consequently, investment happens to be counter-cyclical in the face of LTI shock. However, due to an increase in aggregate consumption, output increases. Working hours are also pro-cyclical. The results show that the easing of macro-prudential regulations induces consumption-led growth in the economy.

The on-impact response of different variables is sensitive to the degree of financial depth. The low level of financial depth enhances the magnitude of pro-cyclical responses and reduces the severity of counter-cyclicality in variables. However, its impact on the persistence of shock is not remarkable. This is not the case for models analyzing the impact of different levels of financial inclusion. The impact of easing the LTV on key macroeconomic aggregate is sensitive to the extent of financial inclusion. An expansionary macro-prudential shock induces output to increase marginally, only in case of full financial inclusion. The cyclical behavior of variables induced by macro-prudential shock is largely dampened in the low-inclusion cases (Figure 8).

Figure 8

LTI shock for varying degrees of financial depth (left) and access (right).

Due to the favorable shock to LTV ratio (mentioned in equation (18)), entrepreneurs’ borrowings increase and converge to equilibrium after the fourth quarters. Investment, working hours, and loans are pro-cyclical, while aggregate consumption is counter-cyclical. The FD occurring through an increase in financial depth only affects the on-impact response of the variable shock which is generally high in case of low financial depth. Otherwise, a financial system with medium and high levels of financial depth moderates positive financial innovation (Figure 9).

Figure 9

LTV shock for varying degrees of financial depth (left) and access (right). Source: Impulse responses are retrieved from Dynare.

From the general overview of the results, a few findings are worth mentioning. Financial depth is an important factor in mitigating the negative impact of both nominal and real shocks. It also increases the favorability of productivity shocks for the economy. However, favorable shocks originating from FS are better realized in an environment with low financial depth. Similarly, adverse shock originating from FS is better mitigated in a low financial depth environment. Another important finding of the study reveals FS as a shock absorber in the case of both nominal and real shocks, however, a catalyst for financial shocks.