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each person’s income. Through the empirical analysis, it is verified that trust has a significantly positive impact on individual income.
This paper is structured as follows. In Section II we present the two modified models and their implications. In Section III, we describe the survey data and present basic descriptive results. In Section IV we test the models’ predictions with empirical analysis both on macro and micro economic performance level, and finally, Section V concludes.
II. The Theoretical Models A. The Modified RBC Model
Consider an economy consists of a large number of identical, price-taking firms and a large number of identical, price taking, infinitely lived households. The inputs to production are capital (K), labor (L), and technology (A). Each period, a constant growth rate 𝑔 and a disturbance constitute the growth of the technology. The production function is Cobb-Douglas, and the output in period 𝑡 is
(1) 𝑌𝑡 = 𝐾𝑡𝛼(𝐴𝑡𝐿𝑡)1−𝛼, 0 < 𝛼 < 1,
(2) 𝑙𝑛𝐴𝑡 = 𝐴̅ + 𝑔𝑡 + 𝐴̃𝑡.
Output is divided among consumption (C), investment (I), and government purchase (G). Each period, fraction 𝛿 of capital is depreciated. Therefore, the capital stock in each period 𝑡 + 1 is
(3) 𝐾𝑡+1 = 𝐾𝑡+ 𝐼𝑡− 𝛿𝐾𝑡.
For firms are price-taking participants in the perfect competitive market, both labor and capital are paid with their marginal products. Thus the real wage and interest rate are
(4) 𝑤𝑡= (1 − 𝛼) ( 𝐾𝑡
𝐴𝑡𝐿𝑡)𝛼𝐴𝑡,
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(5) 𝑟𝑡= 𝛼(𝐴𝑡𝐿𝑡
𝐾𝑡 )1−𝛼 − 𝛿.
The representative household maximizes their expected value of utility function,
(6) 𝑈 = ∑∞𝑡=0𝑒−𝜌𝑡𝑢(𝑐𝑡, 1 − 𝑙𝑡)𝑁𝑡
𝐻. (7) 𝑢𝑡 = 𝑙𝑛𝑐𝑡+ 𝑏𝑙𝑛(1 − 𝑙𝑡), 𝑏 > 0
𝑢(∎) is the instantaneous utility function of the representative member of the household, and 𝜌 is the discount rate. 𝑐𝑡 is the consumption per member for the household, and 𝑙𝑡 is the labor supply per member (for simplicity, the time endowment per member is normalized to 1). 𝑁𝑡 is population and 𝐻 is the number of households in the economy; therefore 𝑁𝑡
𝐻𝑡 is the number of members of the household. For simplicity, we assume in the model that 𝑁𝑡
𝐻𝑡 = 1, i.e. only one member in each household. Population grows exogenously at a constant rate 𝑛:
(8) 𝑙𝑛𝑁𝑡 = 𝑁̅ + 𝑛, 𝑛 < 𝜌.
Assume all households can participate in a non-discriminative bond market with the help of agents，thus households can allocate their income either on current consumption for instant utility at period 𝑡, or they can invest a fraction of their income in the bond market for future consumption. Nevertheless, it is assumed that the bond market is not risk-free and agents in the bond market may choose to cheat their clients with the probability 𝜇 (0 ≤ 𝜇 ≤ 1). We consider the probability of successful investment 1 − 𝜇 as a proxy for the society’s objective trust level and assume the representative household has the full information about the overall risk in the bond market. The intuition for this hypothesis is straightforward that other things being equal, with higher social trust, it is reasonable for households to have better opportunity to gain profit
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society, no clients in the bond market will face the risk being cheated and thus 𝜇 = 0. And in a society everyone distrust each other, consumers entering the market will always get cheated by their agents and 𝜇 = 1. For a normal society in real life, the probability will range from 0 to 1, and the higher the cheating probability, the lower the trust level of the society. For each household facing the risk in the bond market, their expected value of the bond revenue equals to (1 − 𝜇)(1 + 𝑟𝑡)𝑏𝑡, where 𝑏𝑡 denotes the amount of money household paid for the bond at the beginning of period 𝑡. Therefore, as a representative household, the budget constraint for each period is(9) 𝑐𝑡+ 𝑏𝑡+1 = (1 − μ)(1 + 𝑟𝑡)𝑏𝑡+ 𝑤𝑡𝑙𝑡, (10) 𝑐𝑡+1 + 𝑏𝑡+2= (1 − μ)(1 + 𝑟𝑡+1)𝑏𝑡+1+ 𝑤𝑡+1𝑙𝑡+1
… …
Substitute the term 𝑏𝑡+1 in equation (9) with equation (10) and rewrite the budget constraint. For one representative household, the maximization problem is
Equation (13) shows that for household’s optimal decision, current consumption is positively related with the cheating probability, and thus negatively related with the society’s trust level. With lower trust level and higher
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cheating probability, rational household will tends to avoid to invest in the bond market and to increase current consumption compared with a high trust-level society. As under the framework of RBC model that society can only accumulate capital through private investment, the implication is rather straightforward that economy will suffer from underinvestment in a low trust-level society.
The model above however cannot be further solved as it contains a mixture of linear and log-linear ingredients. To simplify the situation, we make two changes to the model: we eliminate government purchase and assume that fully depreciation in each period. Therefore, the evolution of capital stock and the determination of the real interest rate follows the pattern
(15) 𝐾𝑡+1 = 𝑌𝑡− 𝐶𝑡,
(16) 𝑟𝑡= 𝛼(𝐴𝑡𝐿𝑡
𝐾𝑡 )1−𝛼− 1.
Consider 𝑠𝑡 denotes the saving rate for a representative household. Because household can only save to invest or to consume instantly in the period 𝑡, we have
(17) 𝑐𝑡= (1 − 𝑠𝑡)𝑌𝑡
𝑁𝑡.
Substitute both equation (16) and (17) into the household optimization condition equation (13), we have
(18) − ln [(1 − 𝑠𝑡) 𝑌𝑡
𝑁𝑡] = −ρ + 𝑙𝑛𝐸𝑡 α(1−μ)(
𝑌𝑡+1 𝐾𝑡+1
⁄ )
(1−𝑠𝑡+1)(𝑌𝑡+1 𝑁𝑡+1
⁄ ), or
(19) −𝑙𝑛(1 − 𝑠𝑡) = −ρ + lnα + ln(1 − μ) + n − 𝑙𝑛𝐸𝑡(1 − 𝑠𝑡+1) − 𝑙𝑛𝑠𝑡. For equation (19) has to holds for every time period 𝑡, there must be a constant saving rate 𝑠̅ that satisfies the condition. Therefore, substitute both 𝑠𝑡 and 𝑠𝑡+1 with 𝑠̅, the equation (19) becomes
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(20) ln(𝑠̅) = 𝑙𝑛𝛼 + ln(1 − 𝜇) + 𝑛 − 𝜌, or
(21) 𝑠̅ = (𝛼 + 1 − 𝜇)𝑒𝑛−𝜌.
Now consider equation (14), as 𝑐𝑡 = 𝐶𝑡/𝑁𝑡= (1 − 𝑠̅)𝑌𝑡/𝑁𝑡 , we can compute that
(22) 𝑙𝑡= 𝑙 = 1−α
(1−α)𝑏(1−𝑠)= 1−α
(1−α)𝑏[1−(𝑙𝑛𝛼+ln(1−𝜇)+𝑛−𝜌)].
Equation (21) and (22) have important implications how trust affect the consumption and labor supply of the representative household. Both equations indicate that the representative household tends to save more and work more with higher trust level of the society. As households’ income can only come from wages and bond revenues, a society with higher trust level implies better income level for households. In turn, as only households provide investment and labor supply for the firms, the production of the economy will benefit from higher trust level.
To see the effect of trust on the economy directly, substitute 𝐾𝑡 = 𝑠̅𝑌𝑡−1 and 𝐿𝑡= 𝑙𝑡𝑁𝑡 into the production function; thus
(23) 𝑙𝑛𝑌𝑡 = 𝛼𝑙𝑛𝑠̅ + 𝛼𝑙𝑛𝑌𝑡−1+ (1 − 𝛼)(𝑙𝑛𝐴𝑡+ 𝑙𝑛𝑙̅ + 𝑙𝑛𝑁𝑡).
Backward the equation (23) for one period and combine both equation (23) and (24); let 𝑔𝑡𝑌 denotes the growth rate of production in period 𝑡, thus (24) 𝑙𝑛𝑌𝑡−1= 𝛼𝑙𝑛𝑠̅ + 𝛼𝑙𝑛𝑌𝑡−2 + (1 − 𝛼)(𝑙𝑛𝐴𝑡−1+ 𝑙𝑛𝑙̅ + 𝑙𝑛𝑁𝑡−1), (25) 𝑙𝑛𝑌𝑡− 𝑙𝑛𝑌𝑡−1 = ln (1 + 𝑔𝑡𝑌) = 𝛼(𝑙𝑛𝑌𝑡−1 − 𝑙𝑛𝑌𝑡−2) + (1 − 𝛼)(𝐴̃𝑡− 𝐴̃𝑡−1+ 𝑔 + 𝑛).
Equation (23) suggests that the level of output is positively related with both the saving rate and household’s labor supply, thus is positively related with a society’s trust level. However, equation (25) shows that the growth rate of the output is only affected by the growth rate of population and technology, as
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both the output level in period 𝑡 − 1 and 𝑡 − 2 will be certain historical information when predicting the economic performance in period 𝑡. Both equations suggest that trust has only level effect but no growth effect on the output of the economy. A society with high trust level will experience better output level and thus better welfare for the households. Nevertheless, the growth rate of the output will not be affected by the trust level of certain economy.
B. The modified AK Model
The pitfall with the modified RBC model is that the result of no growth effect of personal investment, thus our trust indicator, is ultimately determined by the assumption of diminishing returns of the reproductive factors embedded in the production function. Thus it would be arbitrary to exclude the possibility of growth effect from trust. In this part, we provide a simply modified AK model with household optimization that trust actually provide certain growth effect.
Consider an economy consists of a large number of identical, price taking, infinitely lived households. The inputs to production are period-changing capital (K), and technology (A) which is assumed constant. The production function is a linear function of the capital stock that,
(26) 𝑌𝑡 = 𝐴𝐾𝑡, (A>0, A is constant).
In the economy, output is divided among consumption (C) and investment (I). Each period, faction 𝛿 of capital stock is depreciated.
In contrast with the RBC model, because labor is no longer an input factor in the production function, the representative household optimize their life-long welfare only by properly allocating their income between investment and consumption in each period. The utility function for each representative
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household is set as
(27) 𝑈 = ∑ 𝛽𝑡 𝑐𝑡1−𝛼−1
households in the economy; therefore 𝑁𝑡
𝐻𝑡 is the number of members of the household. Similar as the RBC model, we assume 𝑁𝑡
𝐻𝑡 = 1 for simplicity Following our trust setting in the RBC model, we hence assume that
households face a risky investment market where they will be cheated by their agents with probability of 𝜇 (0 ≤ 𝜇 ≤ 1). Thus their expected total income equals to (1 − 𝜇)[𝑦𝑡+ (1 − 𝛿)𝑘𝑡], where 𝑦𝑡 is the per capita income from investment and (1 − 𝛿)𝑘𝑡 is the capital stock after deducting the
deprecation. The budget constrain of the representative household for each period is
(28) 𝑘𝑡+1+ 𝑐𝑡 = (1 − 𝜇)[𝑦𝑡+ (1 − 𝛿)𝑘𝑡].
For a representative household, the maximization problem is
(29) Max 𝑈 = ∑ 𝛽𝑡 𝑐𝑡1−𝛼−1
1−𝛼
∞
𝑡=0 ,
(30) s.t 𝑘𝑡+1 + 𝑐𝑡= (1 − 𝜇)[𝑦𝑡+ (1 − 𝛿)𝑘𝑡].
Use the Lagrangian to solve the optimization problem, and the first order conditions for 𝑐𝑡 and 𝑘𝑡+1, respectively, are
Combing both equation (32) and (33), we have the necessary condition for household optimization that
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The result of equation (34) shows that with higher social trust, i.e. higher value of (1 − 𝜇), the share of consumption in the next period against the current consumption is higher. Because the technology level is fixed in our production function, the only way to increase future consumption for
representative households is to sacrifice their current consumption and invest more. Hence, the implication of equation (34) is consistent with our findings in the modified RBC model that households tends to invest more in a society with high trust.
For the simplicity of our analysis, we only solve for the constant growth path so we don’t need full policy functions. Let 𝑔𝑡𝑦, 𝑔𝑡𝑐, and 𝑔𝑡𝑘 to denote the growth rate of per capita income, consumption and investment. With the condition from equation (34), we have the consumption growth rate equals to (35) 𝑔𝑡𝑐 = (𝑐𝑡+1
𝑐𝑡 ) − 1 = {𝛽(1 − 𝜇)[𝐴 + (1 − 𝛿)]}1𝛼− 1.
Because the capital stock per capita in our model is solely determined by the investment and deprecation, we have the physical capital growth rate at (36) 𝑔𝑡𝑘 =𝑘𝑡+1−𝑘𝑡
𝑘𝑡 =𝐴𝑘𝑡−𝑐𝑡−𝛿𝑘𝑡
𝑘𝑡 = 𝐴 −𝑐𝑡
𝑘𝑡− 𝛿.
Notice that under the assumption of constant growth rate of capital, the value of 𝑐𝑡
𝑘𝑡 needs to be constant. Therefore, in a stationary state growth path, 𝑔𝑡𝑐 = 𝑔𝑡𝑘 = 𝑔𝑡𝑦 = 𝑔∗. Combining both the equation of (35) and (36), we solve
Hence, the growth rate of physical capital and income per capita equals to (38) 𝑔𝑡𝑘 = 𝑔𝑡𝑦 = 𝐴 −𝑐
𝑘− 𝛿 = {𝛽(1 − 𝜇)[𝐴 + (1 − 𝛿)]}
1
𝛼− 1 = 𝑔𝑡𝑐.
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The result of equation (38) suggests that with higher social trust level, the accumulation of physical capital and more importantly, the economy grow faster, i.e. that trust has growth effect. As the output of the economy is a linear function of the level of physical capital under the specification of AK model, the growth effect of trust will also promise the income effect. Notice the implication of equation (38) is dramatically different from the result of our modified RBC model. The mathematical results of our modified AK model suggest that trust has both output and growth effect, while the modified RBC model indicates that trust should only have income effect.
To sum up, the two models in which households face risky investment market provide several important insights about the economic effect of trust that needs to be tested in our later empirical analysis:
a. Both model suggest that a higher trust level will encourage households to increase private investment. In the long run, such decision will benefit the households with better welfare level.
b. Both model suggest that an economy with higher trust level, benefit from higher private investment, will produce a higher overall output, i.e.
that trust should have income effect.
c. The growth effect of trust is ambiguous. The modified RBC model suggests that growth rate of the output of certain economy is not
affected by the trust level in that society, while the modified AK model, on the contrary, indicates that trust has growth effect.
III. Data
A. Measuring Trust
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The most important step in testing the prediction of the model is to identify a reliable measure of trust. For cross-country data, we use the measure based on the data from the sixth wave of World Value Survey (WVS) conducted from year 2010 to year 2014. The advantage to use the latest wave of the WVS data is that we can includes as many as the number of the countries in our
estimation and it helps to see the general trust effect on economy in different countries, the drawback is obviously that it may mess with the causality in the equation with the time lag between trust indicator and countries’ economic performance. Nevertheless, literature in the past cautiously consider trust is less sensitive to time, or in other words, generalized trust is stable over time (Bjørnskov, 2007); in Keefer and Knack’s estimation (1997, p. 1267), they find “ trust value for 1980 and 1990 are correlated at .91” and “changes in trust over the decade are uncorrelated with growth rates”. Thus these findings imply that trust however can be viewed as a slowly-changed characteristic of certain society in a quite large time scale.
The question used to access the level of trust for a certain country is:”
Generally speaking, would you say that most people can be trusted or that you need to be very careful in dealing with people”. The trust indicator we use in the paper is the percentage the respondents in each country replying “Most people can be trusted”. This trust indicator we use follows Zak and Knack’s framework when testing the trust’s growth effect in their 2001’s work, and since then many other researches concerning the subject of general trust also pick the same trust indicator. Furthermore, Knack and Keefer (1997) provide empirical support for the validity of these data and find that values for trust is consistent with lab experiment results and case study across countries.
For Chinese data, we use the measure based on the data form the Chinese
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General Social Survey (CGSS) conducted in year 2003, 2005, 2010 and 2013.
The question used in the survey to measure trust level is that “Generally speaking, how do you trust the strangers” in the year 2003 and 2005; and for year 2010 and 2013, the question is “Generally speaking, would you say that most people can be trusted”. Different from the World Value Survey, the Chinese General Social Survey measures the intensity of individual’s trust beliefs on a scale from 1 to 5, in which “1” means that strongly distrust and
“5” means strongly trust. With this trust intensity data, we are able to estimate the relationship between trust and individual income. Furthermore, we use the mean value of individuals’ trust in each province as the trust indicator on province-level and then test the trust effect on macro economy performance as our theoretical models predict.
One problem with using survey data to represent and compute society trust level is that the survey can only capture the subjective trust level of
individuals. Though using mean value can predict the average trust level for all individuals in the society by eliminating the impact of certain individual’s subjective deviation from the society trust, it is still necessary to verify that if the mean of subjective individual trust is a good proxy for the overall society’s objective trust level. Aiming this, we provide a Monte Carlo simulation based on a simplified trust model to test the relationship between the individuals’
subjective mean trust value and the society’s objective trust level.
In order to realistically imitate the mechanism of how real social trust works, the simulation model includes the randomness of the individual’s trust, the way subjective social trust is established, and the mutually adjustment of trust levels between society and individuals. In the trust model for the purpose of simulation, we use a uniform distribution between 0 and 1 to randomly
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generate the initial trust level of individuals. The subjective trust level, is calculated using the individuals’ average. And the key adjustment mechanism is represented with a one-time Bernoulli trial as an approximation for the individual investment.
The simulation starts with only one individual. The system first generates a random number between 0 and 1 for the individual to represent the born trust level. Thus at the start, the subjective social trust equals to the individual trust, as it is calculated as the individuals’ average in the whole society. Later the first individual do the one-time Bernoulli trial with the success probability equals to the objective social trust given in advance. Recall the models in Section II, as all households face a non-discriminative investment market, the probability for successive investment equals to the objective trust level, or more specifically 1 − 𝜇. If the investment trial succeeds, the individual will increase his trust but no more than the ceiling limit of the uniform distribution.
The process of the increase will be generated by the system randomly within the uniform distribution. If the investment trial fails, the individual will decrease his trust level randomly, in the same way with a result of success investment. With the adjustment of the individual’s trust, the subjective social trust will in turn be calculated again. Following the same process, the system includes more individual for one person each time and repeat the loop
continuously. Under this framework, we are able to investigate the dynamic of subjective social trust and compare it with the exogenous objective trust level.
Figure 1 shows the logic of a single loop for the process,
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Figure 1 the Simulation Process
Figure 2 shows the simulation results with the success probability value, i.e.
the objective social trust, set at 0.2, 0.6 and 0.9. The line from bottom to top are the results for success values set at 0.2, 0.6 and 0.9, showing the dynamic values of subjective social trust level during the simulation. The results show that the system equilibrium for average subjective trust level is critically determined by the success level. With higher success level or social trust level, the mean value of individuals’ subjective trust tends to be higher than it in a low social trust level society. The confusion of the result is that the average subjective though accurately reflect the rank of the objective trust, the value of the average subjective trust is not exactly the same as the objective trust given.
This problem lies in the fact that for the simplicity of the simulation, the born trust level of individuals is randomly generated using the uniform distribution and not affected by the objective social trust; that is to say, only the mutual relationship between individuals and social trust is included in the simulation, but the mutual relationship between individuals is neglected. Anyway, the focus of the simulation is to test whether average subjective trust can be a proxy for the objective trust, and as long as the rank of trust is not affected, it is reasonable to use mean value of individuals’ subjective trust survey data as
I. Individual Trust
II. Subjecitve Social Trust
III. Bernoulli trial IV. Individual
Adjustment V. Subjective
Social Trust Adjustment
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an approximation for the objective social trust level. Therefore, the trust data from both WVS and CGSS can be confidently used in our estimation.
Figure 2 Simulation Result for Different Social Trust Level Notes: From bottom to top, the values of social trust are set at 0.2, 0.6 and 0.9.
B. Other Data and Estimation Model
To investigate the trust effect on the macro economic performance, we use both cross-country data and Chinese province data to test the predictions of
To investigate the trust effect on the macro economic performance, we use both cross-country data and Chinese province data to test the predictions of