Price Stickiness, Input–Output Linkages, and Monetary Policy Transmission in Korea

2.1 Households

The representative household maximizes

where β∈(0, 1) is the subjective discount factor, C _t is consumption, N _t is hours worked, υ _t is an aggregate preference shock, M _t is the nominal money stock, and P _t is an aggregate price index. The total time endowment is normalized to one, and therefore 1−N _t represents leisure time. A one-period lag term of consumption represents external habit formation in consumption, which is introduced to capture sluggish adjustment in household consumption. It is assumed that the population size, which is normalized to one, does not change.

Consumption is an aggregate of all available goods

where h = {1, 2, …, H} denotes production sector, and C _h,t is the household’s consumption of goods produced in sector h. In turn, C _h,t is

C _h(l),t is the household’s consumption of goods produced by firm l in sector h. ϵ _h >1 is the elasticity of substitution between goods produced in sector h. As is well known, the elasticity of substitution is one for the Cobb–Douglas function. Therefore, this setup implies that goods produced in the same sector are better substitutes than goods produced in different sectors. The weights ω h C represent the share of the household’s consumption expenditures on goods and services produced by sector h.

The aggregate price index P _t is defined as

where

P _h(l),t is the price of the goods produced by firm l in sector h. P _t is the price index encompassing the bundle of goods consumed by households, and thus, it can be interpreted as the consumer price index (CPI).

The household’s labor supply is the aggregate working hours it supplies to each firm in each sector as follows

where γ>0 is a parameter that determines the elasticity of substitution between sectoral working hours and N _h,t is the hours worked in sector h. In turn,

where N _h(l),t is hours worked for firm l in sector h. The structure of the labor market suggests that the elasticity of labor supply is infinite within the same sector. This means that labor is perfectly substitutable among firms within a sector, which allows for complete labor mobility. In contrast, labor is not perfectly substitutable across different sectors, which limits mobility between them. Consequently, I expect that wages and hours will be uniform across all firms within the same sector but will vary across different sectors. This aligns with our fundamental setup, where firms and products within sectors are homogeneous and thus more substitutable than those across different sectors.

The household’s dynamic budget constraint is

where B _t is a one-period interest-bearing nominal bond and W _h(l),t is the nominal wage paid by firm l in sector h. R _t is the gross nominal interest rate on bonds that come due at time t+1, and Ψ _t is the sum of lump-sum nominal profits rebated from entrepreneurs in the production sectors including wholesale producers and retailers. Other variables are defined as above.

The household enters period t with B _t−1 private bonds and receives interest, profits, and wages. These resources are used to fund consumption and reinvest financial assets. For simplicity, I assume that a government does not exist, or equivalently, that the government imposes a lump-sum tax on households and then transfers it back to them, not generating any real effects.

The household maximizes its utility by choosing optimal sequences {C _h(l),t , N _h(l),t , B _t , M _t } _t=0 ^∞ subject to the sequence of dynamic budget constraints and initial asset holdings. The no-Ponzi-game condition is imposed. The first-order conditions (FOCs) for the household’s problem determine aggregate consumption, hours worked, price of the nominal bond, and money demand. The FOCs are given as follows:

In Equation (9), the Lagrange multiplier ϱ _t denotes the marginal utility of the budget constraint. Equation (10) denotes the optimality condition for labor supply. Equation (11) describes the determination of current consumption relative to consumption in the next period. π _t is defined as P _t /P _t−1, i.e., the gross inflation rate between periods t−1 and t. The FOC for the money stock is the standard money demand function. Since I focus on interest rate rules, it is assumed that money supply will meet money demand all the time at the equilibrium nominal interest rate. The quantity of money can be disregarded because the household’s utility is separable in money balances, and therefore, it has no effect on the rest of the model.

Demand for the consumption goods produced by firm l in sector h is as Equation (12). Φ h , t d denotes sectoral consumption demand shocks.

For the demand function and the definition of the price indices, the relations ∑ h = 1 H ∫ 0 1 P h ( l ) , t C h ( l ) , t d l = ∑ h = 1 H P h , t C h , t = P t C t hold.

2.2 Production Sectors

2.3 Resource Constraint

The value added in real terms of each sector is defined as the real value of total production minus the value of material inputs, as described in Equation (31).

The aggregate production is Y t = ∑ h = 1 H p h , t Y h , t , and the aggregate GDP is Y t gdp = ∑ h = 1 H Y h , t gdp . Equation (32) describes the resource constraint in the economy. The left side represents the real GDP, and the right side implies that gross domestic production can be spent as consumption and investment goods, or in the process of capital stock adjustment.

The equation can be written as Y t gdp = C t + X t , which is the familiar national income identity (dropping the capital adjustment costs).

2.4 Monetary Policy Rule

The central bank is assumed to adjust its nominal policy rate to stabilize inflation and output volatilities, following a Taylor-type interest rate rule. After the Asian financial crisis of 1997-98, the Bank of Korea transitioned from a monetary policy framework using the money supply as the nominal anchor to an inflation-targeting regime. In this regime, the Bank of Korea sets the monetary policy rate to stabilize inflation rate within a predetermined target range (The Bank of Korea 2017, Lee and Park 2022). The central bank in Korea did not adopt unconventional policy tools, such as large-scale asset purchases, after the Global Financial Crisis, which is consistent with a conventional interest-rate-setting monetary policy framework. Although there has been growing demand to pursue broader objectives such as financial and external stability, price stability and output stability remain the core objectives of the Bank of Korea’s monetary policy implementation. In this regard, a monetary policy framework where nominal policy rates are determined based on recent developments in inflation and output is considered appropriate.

The rule takes the form

where R and Y ^gdp are steady-state interest rate and aggregate value added (GDP), respectively. As it is possible to distinguish the gross value added from the gross output, the real GDP is included as an information variable considering the practices of central banks to stabilize GDP instead of gross output. The monetary policy rule allows interest rate inertia, which is reflected in the autoregressive coefficient ρ _R . ɛ _R,t denotes the monetary policy shock, which is a white noise process with mean zero and variance σ R 2 .

2.5 Shocks

The shocks in the model include the preference shock υ _t , the monetary policy shock ɛ _R,t , the sectoral productivity shocks Φ h , t s , and the sectoral demand shocks (consumption shocks) Φ h , t d . Except for the monetary policy shock which follows a white noise process as discussed above, the shock processes are as follows:

where ε v , t , ε h , t s , and ε h , t d represent white noise processes with mean zero and variance of σ v 2 , σ s , h 2 , and σ d , h 2 , respectively.

3.1 Model Parameters

3.2 Production Technology Parameters

I estimate the production functions of the six production sectors following the methodology in Bouakez et al. (2009). Estimates of the production function parameters are generated using the annual data regarding nominal expenditures on the production factors and the level of capital stock for each sector for the period from 2002 to 2019. The nominal expenditures predicted by the model are obtained from the first-order conditions of the firm’s problem with respect to each production factor in equilibrium as follows:

Note that the firm subscripts have been dropped in equilibrium, because firms in the same sector are identical. The right-hand sides of these equations denote the wage bill, total expenditures on material inputs, and the opportunity cost of holding capital stock, respectively. It is possible to construct estimates of Ω _N,h , Ω _K,h , and Ω _Z,h , using the ratios of any two of the three equations and the CRTS constraint, that is, Ω _N,h +Ω _K,h +Ω _Z,h =1. The solution of the system is the estimates of the production function parameters for the corresponding years and sectors. The sample averages of these annual observations are the estimates of Ω _N,h , Ω _K,h , and Ω _Z,h , and their standard deviations are given by σ 2 / T , where T=18 is the sample size and σ ² is the variance of the annual observations.

Estimates are presented in Table 3. Several important features stand out. The estimates reveal significant heterogeneity in production factor intensities across sectors. Specifically, the ranges for each production factor across sectors are as follows: the parameter for labor ranges from 0.119 (Utilities) to 0.344 (Mining), that of capital stock ranges from 0.031 (Construction) to 0.335 (Utilities), and that of material input ranges from 0.386 (Services) to 0.762 (Manufacturing). For the entire economy, the output elasticities are estimated to be 0.251 for labor, 0.181 for capital stock, and 0.568 for material input. The estimation results indicate that material inputs are a crucial component in the production functions across all cases and should not be overlooked.

To compare the estimates to those from the conventional Cobb-Douglas production function which does not include material input, I generate Ω _K,h /(Ω _K,h +Ω _N,h ), representing the output elasticity of capital stock divided by the sum of the output elasticities of capital stock and labor, from the estimated parameters. The values for each sector are as follows: Agriculture 0.35, Mining 0.31, Manufacturing 0.36, Utilities 0.74, Construction 0.09, and Services 0.45. For the entire economy, the figure is 0.42, which is larger than the corresponding values from studies using a single production sector that excludes material inputs and production linkage effects, such as 0.36 (Christiano et al. 2005) and 0.24 (Smets and Wouters 2007). These estimates generally align with those reported in Bouakez et al. (2009) which examined the U.S. economy using a multisector model close to that constructed in this study in terms of the industry composition and the same estimation method for production functions. In the U.S. case, the share of materials ranges from 0.377 to 0.662, making it the largest among the factors of production. Excluding material inputs, the proportion accounted for by capital stocks in the U.S. is as follows: Agriculture 0.35, Mining 0.61, Construction 0.12, Durables Manufacturing 0.24, Non-durables Manufacturing 0.33, and Services 0.36.

3.3 Bayesian Estimation

I estimate the rest of the model parameters via the Bayesian method using sectoral and aggregate quarterly time series for the period from 2002 to 2019. The sectoral data are composed of quarterly series of Producer Price Index (PPI) inflation for five sectors. The commodity-based Producer Price Indices are used to generate the corresponding sectoral inflation series. To be specific, the PPI for Agricultural, forestry, and marine products, Mining products, Manufacturing products, Utilities, and Services are used to produce sectoral inflation series for Agriculture, Mining, Manufacturing, Utilities, and Services, respectively. Although PPIs are not available for Construction for the complete sample period, sector-specific parameters could be identified from the Bayesian approach because the parameters interact with aggregate and other sectoral variables through general-equilibrium set-up.

The aggregate data consists of the quarterly series of the nominal interest rate, GDP, consumption, and the real wage rate. The nominal interest rate is the monetary policy rate that the Bank of Korea determines. Real consumption is measured by private consumption expenditures in the National Accounts. Considering that the total population is fixed in the model, GDP and consumption are computed in per capita terms. The quarterly average of the mid-month population is used as the population series. As the model variables are expressed in the log-deviation from the steady state in the estimation, all series are log-transformed and then detrended via quadratic time trend.

Table 4 presents Bayesian estimation results. As discussed above, a large coefficient on the markup means that the impact of demand pressure in determining inflation is relatively considerable while that of price stickiness is relatively small (I will discuss this in more detail below.). The price is the most rigid in the Services sector, followed by Utilities and Mining. In contrast, the prices are estimated to be relatively flexible in Agriculture and Construction. The smallest value for Services implies that it has the least frequent price adjustment among the six sectors. Looking at parameters regarding the monetary policy rule, the estimated autoregressive coefficient is 0.90, which means that there exists considerable persistence of monetary policy rates. The coefficients on the inflation gap and the GDP gap are estimated at 1.33 and 0.93, respectively. The coefficients on capital stock adjustment costs range approximately from 8 to 17.

Table 5 shows the degree of price stickiness across sectors implied by the estimated Philips curve coefficients. As discussed above, the coefficient on the markup in the forward-looking Philips curve κ _h indicates the impact of the demand pressure for goods produced in the corresponding sector. A greater κ _h means that the current inflation is dependent considerably on the demand pressure and thus relatively less reliant on future inflation, which means relatively flexible price adjustment. It is possible to infer ϑ _h , which denotes the ratio of firms not changing their prices and thus the degree of price stickiness in the corresponding sector, from κ _h =(1−ϑ _h ) (1−βϑ _h )/ϑ _h . As κ _h is inversely related to ϑ _h , the smaller ϑ _h (that is, price is more flexible) would imply relatively larger κ _h . The average duration of prices remaining unchanged is 1/(1−ϑ _h ). For example, prices in Agriculture last about 1.47 quarters, while those in Services last about 5.38 quarters.

The duration of prices can be compared with estimates from previous studies. In this study, the weighted average of price durations of the six sectors is 3.71 quarters, implying a probability of 0.731 of not changing prices in each period.^[3] This is longer than the durations reported in studies using single-sector DSGE models. For example, the implied durations of prices are about 2.5 quarters (0.60) in Christiano et al. (2005) and about 2.9 quarters (0.66) in Smets and Wouters (2007), with estimates for price stickiness parameters in parentheses. At the industry level, the finding that Services exhibit greater rigidity than other sectors aligns with previous estimates based on micro-level data and those from a multisector DSGE model in the U.S. (Bils and Klenow 2004; Nakamura and Steinsson 2008; Bouakez et al. 2009). The price duration in Services estimated in this study (5.38 quarters) is shorter than that reported in the U.S. (9.07 quarters, Bouakez et al. 2009). As a result, overall price adjustment in the entire economy is found to be less sticky in Korea than that in the U.S.^[4]

4.1 Simulation Results: Responses to a Loosening Monetary Policy Shock

Using the estimated multisector economy model, I generate the impulse responses of key sectoral and aggregate variables following the monetary shock that decreases the nominal policy rate by 50 basis points per annum on impact. Panel (A) in Figure 1 displays the impulse responses of sectoral production, which shows that sectoral responses are positively correlated, but their magnitudes differ considerably across sectors. The response on impact is largest in Mining, followed by Construction, Manufacturing, Utilities, Services, and Agriculture. Panels (B) and (C) present the responses of hours worked and material input, respectively, which primarily reflect the increased demand for production factors by firms as demand for the products expands, and therefore their dynamics reveal patterns similar to the output responses. Panel (D) plots the real wage dynamics, which are similar to those of hours worked. The sectoral real wages increase proportionally to the magnitude of the increases in labor demand in each sector, which reflects that the limited substitutability of labor acts as a friction on the reallocation of working hours across sectors. Panel (E) shows the responses of sectoral capital stock, which are very sluggish and subdued compared with those of flow variables. The responses of sectoral GDP are plotted in Panel (F). The difference between GDP and output responses stems from the sectoral material inputs used in the production which are excluded from GDP.

Figure 1:

Impulse responses to a monetary policy shock. Notes: The figures illustrate the dynamic responses of sectoral outputs, hours worked, material input, wages, capital stock, and GDP in response to a loosening of monetary policy shock of 50 basis points per annum. The X-axis represents the number of quarters following the monetary policy shock. The Y-axis denotes the magnitude of responses to the monetary policy shock in log points.

Panels (G) and (H) in Figure 2 show sectoral relative prices and consumption responses, respectively. The decline in the relative price of Services arises because its nominal price is the most rigid among the six production sectors. The increase in nominal service prices is smaller than those in other sectors, and thus, its relative price declines. In contrast, the relative prices of other sectors, whose nominal prices are relatively flexible, rise. The differences in sectoral consumption responses are due to changes in relative prices, which arise from the differences in price rigidities. The responses show that household consumption expands least for goods whose relative prices increase the most. The consumption of the agricultural products even contracts for the first two quarters after the shock. In this sense, the change in the consumption basket composition mainly reflects intra-temporal substitution by households.

Figure 2:

Impulse responses to a monetary policy shock (continued). Notes: The figures illustrate the dynamic responses of sectoral relative prices, consumption goods production, inflation, and markup in response to a loosening of monetary policy shock of 50 basis points per annum. The X-axis represents the number of quarters following the monetary policy shock. The Y-axis denotes the magnitude of responses to the monetary policy shock in log points, except for the inflation whose deviations are expressed in percentage points per annum.

Panel (I) plots the responses of inflation rates to the monetary policy shock. The inflation rates of all sectors increase after the monetary shock, but the increase is more evident in sectors with flexible price settings. In contrast, Services inflation rises less, but it is most persistent. The responses of markups are plotted in Panel (J), which shows that the sectors with relatively rigid prices, such as Services, Utilities, and Mining, record larger declines. This reflects that the markups decrease to a greater extent in sectors with rigid prices as retailers find it difficult to pass through wholesale price increases on to retail prices.

The responses of the interest rates and aggregate inflation rate are plotted in Panel (K) in Figure 3. The response of the nominal interest rate is reduced as a result of the monetary policy easing shock. Since then, the nominal policy rate has gradually returned to the initial level, reflecting the positive inflation gap and GDP gap. As the nominal interest rate falls and the inflation rate rises, the real interest rate decreases, which brings about an expansionary effect on the economy. Panel (L) shows the responses of aggregate output, hours worked, and material input. The capital stock, which is presented in Panel (M), shows slow-moving adjustment, peaking at most five quarters after the shock. Panel (N) plots aggregate GDP and its expenditure components, consumption and investment. The relative deviations of the GDP and its components are consistent with stylized facts regarding business cycles.

Figure 3:

Impulse responses to a monetary policy shock (continued). Notes: The figures illustrate the dynamic responses of aggregate inflation, interest rates, output, capital stock, and aggregate GDP and its components in response to a loosening of monetary policy shock of 50 basis points per annum. The X-axis represents the number of quarters following the monetary policy shock. The Y-axis denotes the magnitude of responses to the monetary policy shock in log points, except for the inflation and interest rates whose deviations are expressed in percentage points per annum.

4.2 The Sources of the Asymmetric Transmission

The expansionary monetary policy shock generates a rise in aggregate demand, which in turn expands aggregate output. This increase is not evenly spread across sectors mainly due to the following reasons. First, the difference in price rigidities across sectors affects the extent to which each industry accommodates the expanded demand by increasing its production. It is expected that the sectors with stickier price-setting would increase their output to a larger extent compared to those with relatively flexible price-setting. Second, sectoral products are demanded, either for building up capital stock or using them as material inputs in their own or other sectors' production as determined by the Input–Output structure of the economy. This implies that production would increase further for the sectors whose outputs are extensively used as material inputs or investment goods in the production processes. These two factors are the sources of the asymmetric transmission of monetary policy as shown in the baseline output response (Panel (A) in Figure 1).

To investigate the operation of the two channels, I simulate the model with one of the two channels deactivated. First, I assume that all industries have the same degree of price stickiness, and therefore, any asymmetric output response stems from the differences in inter-industry linkages and production technologies across sectors. The results are presented in Figure 4. I find that the responses on impact are closely related to the use of produced goods of each industry. To be specific, the larger the portion of produced goods used in production process as material inputs or investment goods, the greater the impact on output due to the expanded demand stemming from the Input–Output linkage effect. The responses on impact are roughly proportional to the share of output used as material and investment goods. For example, relatively large output responses in Mining and Construction reflect that almost all final goods in those sectors are consumed as material inputs and investment goods, respectively.

Figure 4:

Conditional responses: Homogeneous price stickiness. Notes: The figures are simulation results from a model where all six sectors have the same value for the price stickiness parameter, that is, ϑ _h  = 0.731 for all h, reflecting an average price duration of 3.71 quarters. Panel (A) presents the dynamic responses of sectoral output in response to a loosening of monetary policy shock of 50 basis points per annum. The X-axis represents the number of quarters following the monetary policy shock. The Y-axis denotes the magnitude of responses to the monetary policy shock in log points. Panel (B) shows the relationship between the ratio of output in each sector used as material input or investment goods and the sectoral output response on impact.

Figure 5 presents the simulation results from the model in which inter-industry linkages and production technologies are restricted to be symmetric across sectors. The matrices determining Input–Output relations are set as identity matrices, which means that each production sector does not rely on goods produced in other sectors in its production process. For the factor intensity coefficients in the production functions, the estimates for the entire economy are used in all sectors. It is also assumed that the portion of each industry’s output in the household’s consumption basket is 1/6. Because of the symmetry in the production technologies and inter-industry linkages, any differences in output responses would reflect those in sectoral price stickiness. I find that the magnitude of the responses on impact is determined by the sectoral price stickiness. For example, Services, which has the stickiest price-setting, shows the largest output response.

Figure 5:

Conditional responses: Homogeneous production sectors and Input-Output linkages off. Notes: The figures are simulation results from a model where all six sectors have the same production technology and Input-Output linkages across sectors are shut off. The matrices determining Input–Output relations are set as identity matrices, implying that each production sector does not rely on goods from other sectors in its production process. Panel (A) presents the dynamic responses of sectoral output in response to a loosening of monetary policy shock of 50 basis points per annum. The X-axis represents the number of quarters following the monetary policy shock. The Y-axis denotes the magnitude of responses to the monetary policy shock in log points. Panel (B) shows the relationship between sectoral price stickiness and the sectoral output response on impact.

I can infer which of these two sources primarily works for each sector. The relatively large output responses in Mining and Construction stem from the fact that their final products are used mainly as material inputs or investment goods, respectively. In the cases of Manufacturing and Utilities, the responses reflect relatively higher proportions of final products being demanded as production factors. Despite the most rigid price-setting behavior, Services shows relatively subdued responses because a substantial portion of its products are used for final consumption. As prices in Agriculture are most flexible and its final products are not substantially used in the production processes compared to other sectors, its output expansion is smallest.

When sectors are ranked by output response magnitudes, the order in our study is Mining-Construction-Manufacturing-Utilities-Services-Agriculture. In contrast, the order in the U.S. case is Services-Construction-Nondurable Manufacturing-Durable Manufacturing-Agriculture-Mining (Bouakez et al. 2009). A notable feature is that while Services exhibit the largest response in the U.S., they belong to the group with relatively smaller responses in our study. In the U.S., the degree of price rigidity in the service sector significantly exceeds that of other sectors, resulting in the largest response despite services being used primarily as consumption goods. In Korea, the difference in price rigidity between services and other sectors is smaller, so the effect of the industrial linkage outweighs the price rigidity effect, resulting in a relatively smaller output response of services.

4.3 Comparison to a Single Sector Model

For comparison purposes, I construct a standard sticky-price DSGE model that features a single producing sector. The production factors in this model include labor and capital stock, but not material input. The factor intensities for labor and capital stock are derived from the estimates for the entire economy (as reported in Table 3) and are adjusted proportionally to sum to one. The adjusted factor coefficients are 0.581 for labor and 0.419 for capital stock. For price stickiness, the value for the entire economy, which is the average price durations of the six production sectors, is used. To be specific, the price stickiness parameter is 0.731, which means that prices remain unchanged for 3.71 quarters on average (See Section 3.3).

Figure 6 compares the responses of aggregate production and inflation from the multisector model and the single-sector model. In the single-sector model, output and GDP are indistinguishable because no material input is used in the production process. In comparison with the baseline multisector version, GDP shows a slightly larger initial response but it is less persistent. In terms of gross output, the response from the single-sector model is roughly half that from multisector model. The inflation response is nearly double that of the multisector model. This implies that ignoring the Input–Output linkages and differences in price stickiness lead to a downward bias in output response and an upward bias in inflation response.

Figure 6:

Multisector model versus single-sector model. Notes: The figures illustrate the dynamic responses of aggregate production and inflation in response to a loosening of monetary policy shock of 50 basis points per annum in the multisector model (baseline results) and a counterfactual single-sector model. The X-axis represents the number of quarters following the monetary policy shock. The Y-axis denotes the magnitude of responses to the monetary policy shock in log points for production and percentage points per annum for inflation.