The role of structural factors in real interest rate behaviour: A cross-country study

Real Interest Rate (RIR) has a profound impact on the well-functioning of any economy hence a good understanding of its behavior is a key policy element. Using a Keynesian framework, we model and empirically test the relationship of RIR to selected structural variables namely inequality, dependency, financial depth, and institutional set up. We employ a panel dataset comprised of 115 countries with annual frequency from the period 2000 to 2018. Considering the structure of the dataset and possible endogeneity in the model; System GMM is used to estimate regressions parameters. We found that inequality and dependency do not have a significant influence on RIR. Financial development contributes to improving efficiency while institutional set up


Introduction
Real interest rate (RIR) is a critical variable in any country growth episodes. Though this concept might be complex and multi-dimensional; but in this paper we could simply consider it as cost of unemployed capital (opportunity cost of money) -we use formulation from World Bank World Development Indicator Database in which RIR is nominal deposit interest rate minus inflation. That is our study is focused more on short term interest rate. It has a critical role as signaling device to where (which economic sectors) and by how much scarce capital is allocated. In globalized world like today, the allocation range is greatly expanded to include which countries. Allocated capital in turn will determine the shape and pace of a country growth. Therefore, it should be in prime interest of every government to understand the behavior of RIR so, they can monitor, and policy managed its RIR.
There are quite substantial competing theories on behavior of RIR (Schmelzing, 2020). Here, we emphasize the role of structural factors on real interest rate equilibrium determination. We have a strong belief that the structural factors have substantial explanation power to explain the behavior of real interest rate. Our belief is shared among others by Carvalho, Ferrero, & Nechio (2016) and Lunsford & West (2017).
In this study we mainly contribute to existing literature through more elaborated empirical model and estimation that highlight the role of key structural factors namely Inequality, Dependency, Financial Depth and Institutional Set Up. These variables of interest are among most important structural factors in determining RIR (Bean et al., 2015 andBorio et al., 2017). The variables of interest are then complemented with control variables; standard in RIR modelling namely Business Cycle, Inflation Risk and Current Account Balance. This regression structure constitutes our baseline model. We elaborate the model by estimation of (a) impact from country income classification, (b) in-teraction terms between business cycle and structural factors and (c) including possibility two global interest rate regimes. The study period includes Global Financial Crisis episode: year 2008; that would serve as cut off for two RIR regimes (as pointed out by Blanchard, Furceri, &Pescatori, 2014 andTaylor &Wieland, 2016). The first regime is perhaps the more "normal" regime; the other is "relatively" low interest rate regime. To the best of our knowledge, this paper offers one of the most elaborate and comprehensive design on RIR empirical works. This elaborate empirical scheme would enable us to comprehend RIR behavior from various perspectives.
We assemble our annual frequency dataset to cover 115 countries from period: 2000 to 2018 (2185 observations). We employ a variant of Dynamics Panel Data (DPD) econometrics technique called System GMM (Blundell & Bond, 1998) to estimate the regression parameters. This technique is chosen since endogeneity and RIR time persistence might be present in the empirical design; hence standard least squares-based panel econometrics would potentially lead to bias result (Nickell, 1981).
The paper will be structured as follows; after this introduction we present a brief recent literature on equilibrium real interest rate (and the research questions) in section 2. Dataset and Methodology will be described in section 3. In section 4, we will report and discuss key empirical findings including diagnostic statistics and robustness check. Lastly, conclusion will be presented in section 5.

Hypotheses Development
Real Interest Rate (RIR) is quite an old concept in economics. Perhaps one of earliest systematic study on this topic could be traced back to famous Fisher (1930) equation in which real interest rate is the difference of nominal interest rate with inflation. Wicksell (1936) proposed the idea of natural short-term interest rate (RIR which is aligned with a full employment output) which has become one of critical concept in macroeconomics.

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We can also relate the real interest rate to the theory of neutrality of money. From perspective of neutrality of money; RIR should be constant and be determined by real factors and the role of monetary factors should be zero on average. The theoretical foundation of neutrality of money could be traced to Hume (1955). Patinkin (2016) emphasized the "still" relevancy of neutrality of money in modern context. Analyzing real interest rate behavior assuming neutrality of money could be viewed as a character of classical school of economics.
Another perspective is Keynesian; this school of thought emphasizes non neutrality of money due to market imperfection. The most common cited cause of imperfect mechanism is price rigidity; both in goods and labor market (Stiglitz & Greenwald, 2003). Woodford (2003) and Gali (2015) proposed equilibrium real rate concept as the real rate of return to keep the economy's output to its potential. Holston, Laubach, & Williams (2017) further defined natural short-term interest rate as real short-term interest rate that aligned with natural rate and constant inflation expectation.
The neutrality of money assumption; a key determinants of equilibrium real interest rate behavior is still hotly debated (Walsh, 2010). Theoretical and empirical literature on real interest rate from both schools is quite extensive. One can view from Classical, Keynesian or even hybrid perspective (Borio et al., 2017 andSchmelzing, 2020). There is a wide spectrum to view the mechanic of real interest rate, hence the topic is well open for further investigation.
In this paper, we study real interest rate (RIR) in Keynesian perspective since we believe there is significant market imperfection stemming especially from structural factors. This market imperfection could arise from various factors, this paper focus on Inequality, Dependency, Financial Development and Institutional Set Up. However, we still must consider the heavy influence of macro-economic factors as shown by a host of empirical works (Garratt et al., 2006). Justiniano & Primiceri (2010) studied the behavior of equilibrium real interest rate using New Keynesian model and US quarterly macro-economic data (covering period from 1962 to 2008). They found the RIR behavior to be stylized with a substantial degree of time variation (and sometimes can be negative). Similar finding is also found by Holston et al. (2017) using greater data coverage: four developed countries (US, UK, Euro and Canada) and quarterly macro data from 1972-2016. Their study added insights that there exists a common driver of RIR globally (akin to spill over mechanism) in addition to country specific factors.
Integration to global market is another important business cycle factor. Bernanke (2005) forwarded saving glut hypotheses; in which the tendency of developing economies to save more has caused declining trend in global interest rate. Caballero, Farhi, & Gourinchas (2008) provide theoretical ground of this hypothesis. Subsequent works by Rey (2016) andDel Negro et al. (2017) provide empirical supports for possible different RIR regimes. Holston et al. (2017) point out that policy response to Global Financial Crisis might accelerate the process of transition to lower RIR equilibrium at least for advanced countries. Despite global trend toward moderation, RIR remains a time persistence phenomenon domestically (Rudebusch, 2002;Schmelzing, 2020).
H 1 : RIR exhibits time persistence behavior and possibly regime variant relationship with macro-economic variables Rachel & Smith (2015) argued that rising inequality should have ambiguous effect to real interest rate. One transmission is negative to RIR in which rising inequality could reduce demand of capital as voters would push political agenda for increased tax to improve wealth distribution. On the other hand, Inequality could push people to work harder and take more risky ventures. This would increase demand of capital hence put upward pressure to | 300 | RIR. Empirical works in this topic also reported mixed findings, see Cingano (2014) and Berg et al. (2018).
Demographic especially dependency ratio is an important structural factor. Higher dependency ratio lowers saving; reducing supply of idle capital hence put upward pressure to RIR (Bean et al. 2015;Borio et al., 2017;Lunsford & West, 2019). Nevertheless, Carvalho et al. (2016) based on their simulations study argued that once factoring the population growth, there might be an offsetting effect on RIR rendering the overall impact of dependency ratio ambiguous.
H 2 : inequality and dependency factors have ambiguous effect to RIR Institutional set up and financial development have been considered as major factors in reducing asymmetric information problem in finance (Levine, 2004). Better institutional set up and developed financial sector decrease informational related cost such as adverse selection and moral hazard that subsequently improve financial sector performance (notably its efficiency: cost of intermediation). Improved financial sector efficiency in turn would positively contribute to economic growth. Recent literature highlighted possible nonlinear: inverse ushaped relationship between financial development; that is the impact is only positive up to a certain point (Shen & Lee, 2006;Cecchetti & Kharroubi, 2012;Law, Kutan, & Naseem, 2018).

Method, Data, and Analysis
This study use following sources to construct the dataset: (1) World Development Indicators (WDI): Real Interest Rate (RIR), Real GDP (local currency), Inflation, Current Account Balance, GINI ratio, Dependent Ratio, Financial Depth. (2) World Governance Indicators (WGI): Voice and Accountability, Government Effectiveness, Political Stability, Regulation Quality, Control of Corruption, Rule of Law, Both sources are from the latest version, as time of writing is October 2019, available in World Bank website. In addition; we also use the ratio of income share of top 20 to the rest of population: TB20. The data is obtained from World Income Inequality Database (WIID) from United Nations University (UNU WIDER).
The dataset is of annual frequency. There are 214 countries serves as cross section unit and 19time unit (years); 4066 observations to begin with. We applied cleansing based on criteria of (a) data availability in each country and (b) outliers. We take out country in which data availability for both dependent variable and regressors are less than 70 percent. Next, we do winsorizing at 1 percent level to remove outliers. The final data consists of 115 countries and 19-time unit, 2185 observations. Real Interest Rate (RIR) is the dependent variable in this study. It is measured by subtracting deposit interest rate with inflation rate (measured by year on year percentage change of CPI). Variables of Interest (VIR) regressors are explanatory variables (right hand side of the regression) that are the focus of the study. Our variables of interest are Inequality (GINI or TB20), Demographic Burden (DEPEND), Financial Depth (FIN_DEPTH) and Institutional set up (INSTITUTION).
The GINI Index measures the area between the Lorenz curve and a hypothetical line of absolute equality, expressed as a percentage of the maximum area under the line. Thus, a Gini index of 0 represents perfect equality, while an index of 100 implies perfect inequality. TB20 is the ratio income share of top 20 percent of population compared to the rest. Age dependency ratio (DEPEND) is the ratio of dependents cohorts-people older than 64 and younger than 15-to the working-age population-those ages 15-64. Data are shown as the

Moch. Doddy Ariefianto, Irwan Trinugroho
| 301 | proportion of dependents per 100 working-age population. FIN_DEPTH is calculated by dividing credit to private sector to nominal GDP. We use 7 alternative proxies for country level institutional set up from World Governance Indicators database (constructed based on a methodology developed by Kraay, Kaufmann, & Mastruzzi, 2010). Six of them are dimensions of governance: Voice and Accountability (V_ACC), Government Effectiveness (G_EFF), Political Stability (POL_STAB), Regulation Quality (REG_QUA), Control of Corruption (CONT_COR), Rule of Law (R_LAW). One indicator: INSTITUTION is calculated as simple sum of the six dimensions (this is our baseline indicator). These indicators summarize the views on the quality of governance provided by many enterprises, citizen and expert survey respondents in industrial and developing countries. These data are gathered from several survey institutes, think tanks, non-governmental organizations, international organizations, and private sector firms.
To better identify and measure the role of variables of interests to dependent variable; we use the following control variables (CONTROL): log of Real GDP constant local currency (RGDP_L), Inflation risk-measured by skewness of inflation; 5 years moving (INF_RISK) and Current Account Balance measured as percentage of GDP (CAB). We take control of possible endogeneity of RGDP_L and CAB. Standard macro econometric modelling considers these variables as endogenous (Garratt et al., 2006). This regression model assumes the persistence of real interest rate (possibly in lag 1 or 2) and time fixed effect -the time fixed effect specified as time dummies matrix; i.e. D_2001=1 if year=2001 and 0 otherwise. We model the relationship between dependent variable, lag of dependent variable, variables of interests, control variables and time dummies as linear form. We model the relationship as a linear dynamic form as follows Where is the dependent variable, is the vector of possibly endogenous regressors and is the vector of (assumed) exogenous regressors. The residual of regression is a composite error term comprised of v i is cross section residual component (Fixed and/or Random Effect) and idiosyncratic residual component (e it ). Nickell (1981) shows that estimation of this model using standard panel techniques: OLS, Fixed Effects and/or Random Effect would produce bias result. This is due to inherent demeaning process that creates correlation between regressors and residual. The bias become more pronounced in small T and large N like our dataset.
To overcome the problem, we estimate the model using Dynamic Panel Data (DPD) technique. Considering the nature of our data, the estimation of our equations was carried out using the system generalized method of moments: System GMM (Blundell & Bond, 1998). System GMM was chosen since the structure of our dataset is of small T (=19) and large N (115) and there is possibly dynamics pattern of the dependent variable. The use of system GMM also enable to perform estimation on time invariant variables like income category and interest rate regime. The procedure applied in this paper follows closely Roodman (2009). We will conduct and report diagnostic tests to ensure the reliability of estimations. The tests would cover Hansen over identification test, Arrelano-Bond autocorrelation test and number of instruments. As robustness check we will compare the baseline results with various specification in terms of lag structure, variables transformation, types of standard errors and one or two step estimation.
Equation 1 would be the baseline model. We will elaborate the analysis further as (1) possible different regime before and after Global Financial 2007-2008. It will be treated using Dummy variables before and after GFC as effect to the constant (D_2008 = 1 if year = 2008 or above; zero otherwise). Our treatment on regime dating based on Holston et al. (2017). (2) The impact of different level of country income categories. We reduced the World Bank five Country income categories (Low, Low-Middle, Middle, Upper Middle and High) into three: Low, Middle and High. This is done as to preserve degree of freedom. Only two dummy variables used: Low Income category is used as a reference. We treat country income category as effect to the constant. (3) we will include interaction terms to capture the moderating or accelerating effect between variables. Specifically, we are interested to find the interaction effect between significant control (business cycle) regressor with significant variables of interests.

Results
In this section we present and discuss the estimation results. First, we show descriptive statistics and correlation analysis of the variables used in the study. Second, we present the baseline regression results which subsequently followed by their robustness check. Finally, we show the extended model result in the last subsection. Table 1 presents descriptive statistics of variables used in the study. The statistics are number of observations, average, median, standard deviation and percentiles (1 percent, 5 percent, 95 percent and 99 percent). By performing this preliminary analysis on the data, we could anticipate or take notes on potential problems in subsequent advanced work.

Descriptive statistics and correlation
The table consists of two parts; the upper part describes descriptive statistics for main variables while the lower part presents the alternative proxies. Here we can see that all the variables are reasonably well behaved. We don't observe outliers (or leveraged observations) that we should care about.
There are slight variations in number of observations with REAL_RATE is the most complete (2185 observations). Of main variables; FIN_DEPTH and INSTITUTION exhibit somewhat positive skewness: the mean is greater than the median, while REAL_RATE shows a negative skewness. In alternative proxies' part, variables: GOV_EFF, REG_QUAL, CONT_CORRUPT and RULE _LAW are all show positive skewness.
Correlation analysis results in Table 2 convey several notes. Pairwise (Pearson) correlation between FIN_DEPTH and INSTITUTION is remarkably high: around 0.723. Another somewhat high pairwise correlation also observed between FIN_DEPTH -DEPEND and INSTITUTION -DE-PEND. The correlation is -0.541 and -0.522 respectively. This situation seems to have caused multicollinearity problem. Nevertheless, since the main estimator we use is System GMM with orthogonal transformation, it seems that the multicollinearity problem can be manageable. Pairwise correlation in other main variables pose no problem, they are in the range of -0.195 to 0.174. High correlation presents between alternative proxies; it is also not a problem since we only use the variable as substitutes.

Baseline regressions
Our empirical estimates on GINI and DEPEND do not support our hypothesis. They are not statistically significant (Table 3). Further it is interesting that System GMM estimator managed to disentangle the effect of two multicollinearity variables: FIN_DEPTH and INSTITUTION to REAL_RATE. Estimates of FIN_DEPTH is negative and statistically significant (at 10 percent level) in the range -0.016 --0.014. This is aligned with our (and the widely accepted) financial development hypotheses.  The role of structural factors in real interest rate behaviour: A cross-country study   Coeffi cients and standard error (SE) of regressors are presented along with sta s cal signifi cance used: * at 10 percent level, ** at 5 percent level, *** at 1 percent level respec vely.   1a). We further contemplate that the result might be due to incorrect specification. Perhaps it should be modeled as a quadratic form. At low level, improvement of institution set up would enhance market mechanism which subsequently provide fairer return to the investors. Nevertheless, once the institutional set up cross a cut off level; competition take over hence improve market efficiency. This mechanism works to prevent investors to get excessive return. Sahay et al. (2015) also confirmed the above conjecture in their extensive macro cross country study Considering this later view, we find the estimates support our alternative hypotheses. Estimates of INSTITUTION conform a parabolic function: the linear part is positive, while the quadratic part is negative. Coefficients of the linear part is in the range of 0.184 -0.224; while the quadratic part is in the range -0.024 --0.019. Estimates of both terms are statistically significant at 10 percent.
All system GMM estimation report significant coefficients (at 1 percent statistical level) of REAL_RATE lag 1. Coefficients of REAL_RATE at lag 2 are not significant. These results have given support to our initial assumption that REAL_RATE exhibits persistence behavior of order 2 at maximum.
We also obtain evidence a strong macro econometric model style relationship between REAL_RATE, GDPR_L and RISK_INF. Coefficients of GDPR_L are positive in the range of 1.077 -1.306 and statistically significant at 5 percent level. RISK_INF estimates are negative and statistically significant at 5 percent in the range of -0.44 --0.310. Evidence of positive estimates of GDPR_L and negative estimates of RISK_INF; support the Keynesian feature of macroeconomic model in which price level is sticky.
In baseline regressions we also estimate using least squares technique: pooled, fixed effect (FE) and random effect (RE) as comparison purpose. The likelihood ratio statistics of null hypotheses redundant FE (country dummies) is clearly rejected; meaning we should take care for possible effect in the residual. Furthermore, the Hausman statistics of null hypotheses of no correlation between regressors and residuals is also strongly rejected. That means we should cast the regression in a manner that account for possible endogeneity; thus, application of System GMM is warranted.
Diagnostic check for system GMM shows that current specification is appropriate. The F statistics as a measure of overall goodness of fit present a convincing evidence of the statistical importance of regressors in explaining REAL_RATE. The number instruments used is 89; less than number of cross section groups (115). Hansen Overidentification Test report that endogeneity is no longer a statistically significant issue. Lastly, the non-rejection of autocorrelation test at lag 2; provide support to our dynamic specification. All dynamic coefficients of lag dependent variable are less than one in absolute term; hence the proposed dynamic model is stable.

Robustness check
We employ two types of robustness check in this paper. First, we use sequential inclusion of variables of interest and observe whether it has caused substantial changes in the regression results. Secondly, we replace two variables interest: GINI and INSTITUTION with comparable proxies. We replace GINI with TB20 and for INSTITUTION we use 6 alternatives: V_ACC, G_EFF, POL_STAB, REG_QUA, CONT_COR, and R_LAW. Table 4 reports the result of type one diagnostic check. We think our result is quite robust. Estimates and statistical significance for the macroeconomic control variables (R_GDPL, INF_RISK and CAB) are qualitatively unaltered. There is a change in algebraic sign in GINI estimate. Nevertheless, since they are all still not statistically significant; we can address this situation as due to sampling variation.

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Estimates on DEPEND also experienced a change in algebraic sign as we sequentially include the variables of interests. Again, these estimates are not statistically significant hence do not bear significant consequence to the analysis. There are remarkable stable estimates for FIN_DEPTH and IN-STITUTION. These estimates still conform with the findings reported in the baseline model.
We could see that even after replacing proxy GINI with TB20, inequality variable remains statistically significant (Table 5). From six alternative proxies for INSTITUTION, only POL_STAB that is statistically significant (at 5 percent level). However, this estimate is also not aligned with hypotheses hence we test for possible quadratic form. In the latter model, POL_STAB estimates are not statistically significant. This finding provides us with an important insight. INSTITUTION seems to be a complex construct with no component proved to be dominant. Only when it is treated as an integration then the impact to REAL_RATE can be observed (and inferred).
Lastly, we also observed that diagnostic statistics (F statistics, Hansen OIR and Autocorrelation) are also unaltered. Therefore, regressions results could be said relatively robust in specification.

Extended model
There are three ways in which the previous baseline results will be elaborated. First, we test for significance of possible low interest regime after global financial crisis. Second, we include for possible effect of country income categories: low, middle and high. Third, we specify models with interaction terms of macro variables (RGDP_L, RISK_INF and CAB) with (statistically) significant variables of interest (FIN_DEPTH and INSTITU-TION).
The results are summarized and reported in Table 6. Here we obtain estimate of the Interest Regime Dummy (D_2008) is negative (-0.609) and statistically significant at 10 percent level. It is interesting to find that the resulting constant due to D_2008 = 0 is also negative (-20.062) and significant (at 5 percent level). This finding doesn't change our conjecture that real interest rate should be lower in years following 2008. However, it seems to suggest that there is already mechanism working to reduce equilibrium real interest rate across country.
Nevertheless, we should take a note on robustness of this regressions. Including Interest Regime Dummy has increased the Hansen OIR statistics to 85.25 that has caused inability to reject no endogeneity null hypotheses at a convenient 1 percent level.
We find that coefficients of country income categories to be positive but not statistically significant (both the dummies and reference constant: low income countries). This situation could be due to possible correlation with following variables: GDPR_L, FIN_DEPTH and INSTITUTION.
From nine interaction terms we estimated; only one that is statistically significant. Interaction terms coefficient of RGDP_L*FIN_DEPTH is negative (-0.017) and significant at 5 percent. It suggests there exist a dampening mechanism of equilibrium real interest rate from rising due to increasing economic activity; provided by developed financial sector.

Conclusion
Adopting a Keynesian framework; we model and estimate variables affecting Real Interest Rate (RIR). We emphasize the role of structural variable: Inequality (GINI or TB20), DEPEND, FIN_DEPTH and INSTITUTION to the behavior of RIR in addition to standard macro modelling approach.
Both Inequality proxies (GINI or TB20) and DEPEND do not statistically significant influence RIR behavior. The inability of both Inequality and Dependency proxies to significantly explain RIR behavior might be an evidence of ambiguous effect manifestation as outlined by existing literature. Never-The role of structural factors in real interest rate behaviour: A cross-country study Moch. Doddy Ariefianto, Irwan Trinugroho | 311 | theless, we could not also dismiss the possibility of inadequate empirical design as our study limitation. Perhaps better-quality proxies and better econometric techniques could improve estimates; this is an avenue for future research.
Financial development helps improving efficiency as shown by negative and statistically significant FIN_DEPTH coefficients. The impact of IN-STITUTION to RIR follows an inverted U shape. Initially growing institutional set up would increase the return on unemployed capital (opportunity cost of money); working as improving investor protection. After a certain threshold then the impact IN-STITUTION will be negative to RIR (ie. efficiency improving).
Our estimates show that financial sector and institution development could help to reduce RIR; hence improve financial system efficient functioning. Government and regulator should gear their policy toward accelerating developing these two aspects to reach "efficiency" level. Attaining this level would be necessary to lower RIR possibly due to competition effect. In addition, we also find that there is a negative (and statistically) significant interaction term between RGDP_L with FIN_DEPTH. It means higher financial development could have an offsetting effect to procyclicality of RIR.
Analysis on control variables reveals that RIR is a persistent variable and highly pro cyclical. Sticky price hypothesis explains Real Rate behavior better as shown by negative and statistically significant coefficient of RISK_INF. These findings call for prudent macro economy management. RIR is strongly procyclical variable and substantially laggard to inflation realization (sticky price). Therefore, imprudent macro economy policies could have prolonged undesired capital allocation effect (due to higher RIR).
Lastly, there seems to be two different global real interest rate regimes in the study period with year 2008 as a cut off. RIR after 2008 can be considered as the lower RIR regime. This could be beneficial to economic development especially in emerging countries. Emerging countries could tap to the global debt market now to close financing gap that exists domestically.