4.1. Data Description
We employ FCM to analyze the effects of uncertainty shocks on individual household’s savings and working hours. Before constructing the map, we introduce the concepts in our FCM and corresponding data. There are 18 concepts in our FCM and they can be classified into four groups. It is notable that employing FCM facilitates specifying the causal relations between these concepts and analyzing dynamics in the system without inflicting much dimensionality issue.
The concepts in our FCM can be classified into following groups: exogenous concepts, macroeconomic concepts, household state concepts, and household choice concepts. Causal effects between the concepts are organized sequentially following the pre-determined exogeneity order: exogenous concepts, macroeconomic concepts, household state concepts, and household choice concepts in the end. We impose such hierarchical structure in the map following existing literature on the effects of uncertainty shocks. Bloom [
7], Choi and Shim [
4], and Bhattarai et al. [
21] all impose the similar identification in each of their VAR models. They impose Cholesky ordering of variables so that the uncertainty shocks instantly affect macroeconomic variables. Similar to their model design, we set uncertainty shock variables as exogenous concepts that affect all other concepts in our FCM.
Our data include 18 variables consisting of 10 aggregate variables and eight household-specific variables. Our data sources are Economic Statistics System (ECOS) provided by Bank of Korea and Korean Labor Income Panel Study (KLIPS). We additionally collect Korean EPU from the website (
www.policyuncertainty.com). We collect data from 2006 to 2016 and incorporate macro data with 997 individual household panels.
By exogenous concepts, we mean that these concepts serve as the only force in the FCM that drives changes in other concepts. We specify Financial Stress Index (FSI) presented by Cardarelli et al. [
22] and Economic Policy Uncertainty Index (EPU) introduced by Baker et al. [
9] as exogenous concepts. We calculate daily FSI based on the methodology proposed by Cardarelli et al. [
22] using KOSPI log-return rates, KRW-USD nominal effective exchange rates, and interest rates, and take the annual mean of the index. Then, we use Hodrick–Prescott detrended values of the two indices and identify their deviations as annual uncertainty shocks. We assume that the two shocks cause changes to each other interdependently and they together affect rest of the concepts in the map.
We specify eight macroeconomic concepts, which are affected by exogenous variables and, in turn, change the household characteristic concepts. The macroeconomic concepts are consumer sentiment index, lending attitude index designed by Bank of Korea, household borrowing interest rate, inflation rate, unemployment rate, GDP growth rate, KOSPI index, and government expenditure. All variables are annual values. Specifically, lending attitude index reflects banks’ willingness to make loans to firms and households and is collected from a survey. Household borrowing interest rates are borrowing rates for household new loans. Lastly, we include the detrended government expenditure by using Hodrick–Prescott filtered annual deviations in the map to take account of the government’s fiscal adjustments in response to uncertainty shocks.
We also include six household state concepts that summarize individual household’s financial status and two choice concepts that households adjust based on each of their financial situations. Household state concepts include a household’s debt, asset, labor income, financial income, real estate income, and transfer income. We particularly specify four sources of household income to see if different sources of uncertainty affect the income in different ways. Then, we introduce household annual consumption expenditure and average weekly working hours as the household choice concepts. This is to resemble traditional macroeconomic models where households choose consumption and labor supply given budget constraints. One may point out that household’s working hours are labor market equilibrium values and hence they are different from household labor supply. This is precisely why we include macroeconomic variables such as GDP growth rates and unemployment rates in our cognitive map and control possible effects of labor demand on household working hours. All of these concepts except for working hours are in real terms divided by annual Consumer Price Index, respectively.
To sum up, we include 18 macroeconomic and household specific variables from 2006 to 2016 in our cognitive map analysis. Parsimony of FCM in terms of computation enables us to analyze dynamics and relations between these variables. We further describe how each of these variables are converted into concept values and how causal weights are determined in the following subsection.
4.2. FCM Setting and Inference Scheme
As mentioned before, we study households’ consumption and labor supply decisions by constructing an FCM for each household each year. We include 18 macroeconomic and household-specific concepts in our cognitive map. To initialize the inference procedure, we first standardize the variables and convert them into z scores. For household-specific variables, we standardize the variables each year to reflect each household’s relative positions. We then normalize the z scores into values in by plugging them into sigmoid function: .
We then set the weights that specify causal relations between concepts. As described in the previous section, exogenous concepts cause changes in all other concepts while macroeconomic concepts alter household-specific concepts only. Lastly, household state concepts affect the two household choice concepts, consumption expenditure, and working hours. We do not allow for feedback from the household-specific concepts to macroeconomic and exogenous concepts, and impose no autoregressive structure in the process of exogenous concepts. This is because our aim is to design an FCM that represents the decision-making process of each household each year.
We first assign initial weights upon which we build 10,967 weight matrices in total. We conduct regression of each variable with all other variables one at a time, and then employ the standardized regression coefficients as the initial weights between concepts. We conduct regressions separately for each year, so 11 initial weight matrices are assigned for years 2006 to 2016. We first estimate the following regression:
where
is weight of concept
j on concept
i,
i and
j are concept indices, and
h is household index. We augment values of
if the values depart from what the previous studies suggest. Hence, our approach is a hybrid of data-driven and model-driven approaches in terms of designing FCM. A similar, regression-based approach was employed in fuzzy analysis of multiple variables [
23].
Table 1 is the list of concepts and their labels to be used in
Figure 1 and
Table 2.
Table 2 is the mean of 11 initial weight matrices that we assign to our cognitive map. As could be seen in
Table 2, the uncertainty shocks E1 and E2 affect all other concepts in the FCM, though it is surprising that households’ working hours and EPU shocks apparently showed no sign of correlation on data. Effects of uncertainty shocks on each variable matches the conventional wisdom in general, and we set this matrix as the input weight matrix for the weight-updating process.
Figure 1 is a graphical illustration of FCM assigned the mean initial weight matrix. Note that the black and red lines stand for positive and negative causal relation between concepts, respectively. Width of the lines represents the degree of causality, with wider lines drawn for stronger relations.
We update the yearly initial matrices to design FCM for each household via nonlinear Hebbian learning method. We employ the method similar to that proposed by Papageorgiu et al. [
24]. Papageorgiu et al. [
24] suggest the following scheme to update weights. Weights are updated after each simulation step until the sum of two subsequent output concepts’ differences is smaller than some numerical value as small as
.
is the weight of concept
j on concept
i at
n-th simulation and
is concept value of
j at
n-th simulation:
We obtain the weight matrix for each household using Equation (
4) and then use them to predict the household’s consumption expenditure and working hours in the next year. In actual implementation of FCM inference, we choose the rescale inference rule:
Transformation function
is sigmoid function
with
of 1.3. The value of
was selected to maximize the FCM’s in-sample forecasting performance of household consumption expenditure and working hours. We define one iteration step as one year in real time, hence our forecasts of household consumption expenditure and working hours are obtained from the concept values of C1 and C2 after one iteration. A similar forecasting procedure was employed in Gupta and Gupta [
25].
We plug the concept values in the inverse function of sigmoid function:
to obtain forecasts of household consumption and working hours in the next year. By this, we numerically convert the output concept values into real values. Our overall method is summarized in Algorithm 1.
Algorithm 1: Forecasting Household Consumption and Weekly Working Hours with FCM |
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After we obtain forecasts of household consumption and working hours for every household each year, we compute the root mean squared error (RMSE) of the simulated results and the data. RMSE are reported as 6.981 for real consumption expenditures and 11.113 for weekly working hours. We conclude that our approach offers reasonable forecasts for the two household choice variables.