Why is the economic recovery not stimulated even though the central banks offer the sizably low interest rate which is close to zero? Many people imagine that if the interest rate is low, the economy should be stimulated. The reason is that the cost for companies paying the interest rate of their debt and for entrepreneurs planning to borrow money to start their new business is low.
However, this is only the microeconomic factor, which is a static analysis focusing on the individual economic agent's performance, and does not take account of the time effect and the environment interacting with this agent's performance. This means it ignores the macroeconomic factor which is the dynamic analysis taking account of the future expectation and the wide scale economic environment.
The problem is that, even though the interest rate, the cost of borrowing, is low, if the expected return from investing to economy is low, banks and the other forms of financial institutions are reluctant to lend their money. In addition, the entrepreneurs are discouraged from borrowing money to invest to their business if the future expectation is not good for their business due to the current economic environment.
This phenomenon is called the "liquiditytrap" which was originally mentioned by Professor John Maynard Keynes. During the world economic depression in 1929, many economists thought the economy would be eventually recovered if the central bank tried to increase the liquidity of money supplied by lowering the cost of borrowing money. However, this expectation did not happen. Keynes analysed this problem by explaining the liquidity of money was stuck in their flow due to the lack of confidence in investment. Keynes also put emphasis on need of the price inflation to increase the investment volume. If the price inflation is taking place, the real value of the money borrowed at a certain past time period goes down, and the nominal value of the revenue gained at each time period keeps increasing (the real value of the revenue is kept almost constant). By contrast, if the price deflation (i.e. the "minus" inflation) occurs, the financial economic situation is the opposite effect of the inflationary period.
This project assessed whether positive or negative the correlation between the interest rate and the investment share of GDP. London Interbank Offered Rate has been newly introduced by the IMF, WEO Database, Country Data recently so this newly introduced variable was used as the variable representing the interest rate. Although, there are only the US and Japanese one for London Interbank Offered Rate, the USA and Japan are the best candidate countries to assess the effect of the liquidity trap because they are experiencing now! In addition this variable is a very useful indicator of the interest rate effect on economy because this interest rate index takes account of the various money transactions between various banks and the other forms of financial institutions.
* "London Interbank Offered Rate" is denoted as "the interest rate" and "the nominal interest rate" in this project.
* There are two indicators of the investment share of GDP. One is "the percentage investment share of GDP times the (natural) log of GDP", and another is "the (natural) log of the GDP times the percentage investment share of GDP"
* All the logalisms used in this project is the natural log.
* These OLS regression analyses are based on the fixed effect model which involves the dummy variables (the binary variable) for the different units (countries).
* The variable called "Time" denotes the time trend whose valometer increases as the time passes.
First of all, the simple Ordinary Least Squares (OLS) regression analysis was run. The investment share of GDP is regressed on the logged interest rate. The result offered is shown in the figure below:
This OLS regression is the percentage investment share of GDP times the (natural) log of GDP:
This OLS regression is the (natural) log of the GDP times the percentage investment share of GDP:
These results show that the positive correlation between The investment share of GDP and the interest rate. It is really disappointing for those who trust the monetary policy of both the current US Federal Reserve Bank and Bank of Japan. It is also surprising for many microeconomic financial analysts because it indicates that the business grows when the cost of borrowing and the interest payment on companydebt is high. This contradicts the basic static ( = nominal) cost and benefit analysis. Thus, these results affirm that we certainly need a complex dynamic ( = real ) cost and benefit analysis.
Is it logical to say that "We should rather increase the interest rate to recover our economy?" No, this is not logical. It is not logical to say "Higher the cost for companies and entrepreneurs is, higher the confidence of consumption and investment is".
This aspect suspects that the interest rate is not exogenous (the condition to be a good explanatory variable not being controlled by any other factors (variables)) so that it can be endogenous (controlled by some other factors. This situation leads the analysis inconsistent if this endogenous variable is used as an explanatory variable).
There is an international financial economic theory stating that the interest rate is given by the exogenous factor we are hardly able to control rather than we give the interest rate to control the economic situation. This theory suggests that the interest rate is set according the price inflation rate to make the real interest rate (the nominal interest rate minus the price inflation rate) to as zero as possible. Therefore, this theory rejects the classical and the monetarist theory of the interest rate which states that the low interest rate lowers the cost for the entrepreneurs i.e. stimulating the economy. This theory claims that the interest rate is an indicator of the price inflation. It means that, when the interest rate is high, the expected rate of the price inflation, which increases the business opportunities, is high.
* This is the theory in the developed economies where the hyperinflation risk caused by the malfiscal functioning tends to be low.
All in all, there is a room to assume that the inflation rate stimulates the investment share of the GDP. Therefore, it tested if the logged investment share of GDP is positively correlated with both the interest rate and the logged price inflation rate (In the later texts, the price inflation rate is written as the inflation) as follows:


This proves that the inflation is positively correlated with the investment share of GDP. However, there is a concern that the interest rate and the inflation are correlated each other. If the explanatory variables in one OLS regression are correlated each other, it tends to disturb the OLS analysis result.
So, it suggests to assess the endogeneity of the explanatory variable. By following Keynes' theory and the theory claiming the interest rate is given, the interest rate is assumed to be positively correlated to the inflation. This inference also claims that the Two Stage Least Square (TSLS) regression analysis, instead of the OLS, to regress the investment share of GDP. The first stage regression, which is called the "auxiliary regression", to regress the interest rate, the candidate explanatory variable of the investment share of GDP, on the inflation, the instrument variable of the interest rate, the explanatory variable.
The other reason why the inflation is wanted to be used as an instrument variable and the interest rate is wanted to be used as an instrumented explanatory variable is that this project attempted to explain the whole mechanism explained by the theory and assess if this theory actually proves the real world economic situation. Because it assumes that the interest rate is highly controlled by the inflation. Therefore, the inflation had to be used as an instrument variables so that it cannot be used as one of the explanatory variables.

These results proved that the inflation is positively correlated with the interest rate as the theories suggest.
The fitted value of the interest rate instrumented by the inflation rate (and Time if necessary) was saved to use for the second stage regression, which is the primary regression of the TSLS analysis.
There are two analyses because "the percentage investment share of GDP times the (natural) log of GDP" and "the (natural) log of the GDP times the percentage investment share of GDP" are assessed a little bit differently. The former one was regressed on the interest rate instrumented by both the inflation rate and the Time meanwhile the latter one was regressed on the interest rate instrumented by the inflation rate only.
Both kinds of regression analyses are based on the nonlinear model because there is assumed to be the optimum interest rate affected by the optimum inflation rate which maximise the investment share of GDP. The positive but reasonable rate of the inflation is a indication of the circulation of economic activities running well and the economy is expanding not too fast. However, the positive and high inflation rate decreases the real value of individual economic agents' income, and discourages saving, the source of financial economy, and supply of the investment available (The net present value of the amount of money invested declines over time). In addition, as the (nominal) interest rate is determined by the inflation rate (in order to set the real interest rate (the interest rate minus the inflation)). Therefore, in order to find the optimum inflation rate and then the optimum interest rate (= The intercept + Coeff. x "The inflation" + error) are required to find out!
The regressions below are "the percentage investment share of GDP times the (natural) log of GDP" on the interest rate instrumented by the inflation and the time trend:

According to the three criteria (denoting the smaller number shown by each criterion implies the better model), the regression above without including the time trend as one of the explanatory variables is a better model than the other with the time trend as one of the explanatory variables. This reason would be because the time trend is already included in the instrument variable of the interest rate.
The other sorts of models with various kinds of formulae, such as the liner model ( I = a + b x R + error) and the cubic formula ( I a + b_1 x R + b_2 R^2 + b_3^3 + error ), are regressed. Nonetheless, the square formula (The second degree formula) came up as the best model to demonstrate the correlation between the investment rate times the GDP. By observing the both models above, both formulae has the global maximum value. Therefore, this result indicates that the optimum interest rate instrumented by the inflation rate exists.
The figure below contains the matrix graph (the top one) showing what the interest rate given by the inflation and the year is, and the other (the bottom one) showing what "the percentage investment share of GDP times the (natural) log of GDP" given by the interest rate instrumented by the inflation and the time trend is:
These graphs indicate the following phenomena:
# The real interest rate (the gab between the interest rate and the inflation rate) tends to be minimised as the year (Time) passes.
(This could be considered because of the global financial liberalisation which has increased the degree of competitiveness of the global financial market. )
# The optimum interest to stimulate the economic activity is between 1.77 and 2.14.
# In 1980 (and possibly before), the high inflation is discouraged the economic activity level more than the low inflation.
# In 1990 and after, the lower inflation discourages the economic activity level far more than the high inflation.
The regression below assessed "the (natural) log of the GDP times the percentage investment share of GDP" with the same method as "the percentage investment share of GDP times the (natural) log of GDP" assessed in the previous regressions.
For "the (natural) log of the GDP times the percentage investment share of GDP", the interest rate is only instrumented by the inflation because this model needed to include the time trend as one of the explanatory variables. This reason is because the dependent variable "the (natural) log of the GDP times the percentage investment share of GDP" is increasing over time so that the regression model had to involve the explanatory variable explaining this factor. It also had to exclude the time trend from the instrument variable of the interest rate in order to avoid including one same variable for two different indicators.
The figure below contains the matrix graph (the top one) showing what the interest rate given by the inflation and the year is, and the other (the bottom one) showing what "the (natural) log of the GDP times the percentage investment share of GDP" given by the time trend (Exogenous) and the interest rate instrumented by the inflation is:
These graphs indicate the following phenomena:
# The optimum inflation rate stimulating the economic activity is 2.48, and the optimum interest rate is 1.5 then.
# Lower the interest rate is implies lower the economic activity level is.
Having observed these results given by the regression analysis (based on the fixed effect model), the sizably low interest rate is less likely to increase the liquidity of the money supply flowing into economy. As Prof. Keynes suggested, the USA and Japan may need to expect the exogenous shock in their economy, such as technological growth and finding a new natural resource and/or a brand new invention, and/or the strong positive planning policy intervention other than the monetary policy.
All in all, the policy makers cannot merely control the interest rate to expect the economic recovery. Hence, the current US and Japanese monetary policy seems to be very unreliable to stimulate the economic recovery.
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