Nonlinear Relation Between Inflation and Growth – Panel Data Analysis

Table of Contents

1 Introduction

2 Inflation and Economic Growth in Developing vs. Developed Countries

3 Literature Review

4 Motivation

5 Theoretical Background
5.1 Effect of Inflation on the Balanced-Growth Path
5.2 Nonlinearity in the Inflation-Growth Nexus

6 The Methodology
6.1 The Data

7 Results
7.1 OLS
7.2 Panel Regressions
7.2.1 Two-way Fixed Effects
7.2.2 Mean Group Estimator
7.2.3 Common Correlated Effects MG estimator

8 Conclusion and Further Discussion

9 References

10 Appendix

List of Figures

Figure 1 Distribution of Level of Inflation Rate

Figure 2 Distribution of Log of Inflation Rate

Figure 3 Scatterplot of GDP Growth and Log of Inflation

List of Tables

Table 1 Descriptive Statistics

Table 2 Pooled OLS Results

Table 3 Two-Way Fixed Effects Estimation Results

Table 4 Mean Group Estimation Results

Table 5 CCEMG Estimation Results

Table 6 Summary of Threshold Levels

‘Inflation is a disease, a dangerous and sometimes fatal disease, a disease that if not checked in time can destroy a society.’ - Milton Friedman

Abstract

This paper examines the inflation-growth interaction for different country groups with similar national incomes for the period 1970-2011. It could be confirmed that this relation is strictly nonlinear with a threshold level of inflation of 3% for high-income countries and 13% for low-income countries. Although this result is in line with previous empirical studies based on a similar data set, much smaller samples needed to be used to obtain these results. Inflation threshold levels are estimated using the iteration method and different panel-specific tech- niques. Strongly significant thresholds were yielded only when controlling for country-fixed effects. Policymakers can use the findings for high-income or industrialised countries as a guide for inflation targeting, however more precise analyses for less advanced countries are needed in order to be useful for monetary policy.

1 Introduction

The main objective of macroeconomic policy is to achieve high and stable growth and simul- taneously to keep inflation rates at low levels. In consideration of the obvious relation be- tween inflation and growth, many studies have been concerned with examining the nature of this link. After for many years no relation between these variables could be accounted for, the results changed in the 1970s so that it is now univocally accepted that inflation has indeed a negative effect on growth, as it does not allow to allocate resources efficiently by masking the signalling of the role of relative price changes, a crucial guide to efficient economic decision- making (Khan and Senhadji, 2001). This finding was followed by further research on the question, how low should inflation be, or in other words, what is the maximum level of infla- tion until which the relation is positive, but turns negative if inflation rises beyond this thresh- old level. A number of authors in the 1990s identified such a nonlinear relationship between inflation and growth. Sarel (1996) analysed a panel of 87 countries over the period 1970 to 1990 using OLS estimation. He finds a structural break at an average annual rate of inflation of 8%. Below this level, inflation has no significant effect on growth, but for inflation levels above 8%, growth is significantly and strongly negatively affected. Gosh and Phillips (1998) find a much lower threshold at 2.5%, and Christoffersen and Doyle (1998), applying Sarel’s methodology on transient countries between 1990-1996, obtain a threshold of 13%. Bruno and Easterly’s (1998) results are somewhat striking. Their analysis is based on a sample of 31 countries that experienced high-inflation episodes over the period 1961-1994, and results in the fact that inflation does not have a significant effect on growth for normal levels, however the relationship becomes negative with high-frequency data and high-inflation observations of 40% or higher. Khan and Senhadji (2001) contribute to existing work by extending and modi- fying their analysis by, first, looking separately on developing and industrialized countries, and second, by applying new econometric methods, which include the non-linear least squares (NLLS) estimation combined with a hybrid function of inflation, where the threshold level is found with conditional least squares. Furthermore, they use the bootstrap method, proposed by Hansen (1999), in order to test for statistical significance of the threshold effect. Accord- ingly, their results differ in so far from previous work as the threshold levels for industrialized countries are substantially lower than for developing (1-3% and 11-12%, respectively). Apart from these studies, other authors attempted to determine an inflexion point for the growth- inflation relation, however the results remain rather mixed, so that until the present point no consensus exists about which inflation should be targeted by policymakers. Thus the aim of the present work is to shed more light on and clarify which threshold level is appropriate for which country group.

The present paper is devoted to the analysis of the non-linear inflation-growth relationship for a panel of 154 countries over the period 1970 - 2011. This study is in so far different from other studies as I divide this large sample in seven groups of countries with comparable eco- nomic performances. Thereby I am aiming to show that more precise results can be obtained when the different income and development levels are taken into account when testing for the threshold level. As well as this, the present paper analyses over a larger time period, including more recent data from the (post-) financial crisis years that are contributing to new results on this topic. This analysis is carried out by applying an iteration methodology suggested by Sarel (1996), whereby regressions are estimated for different threshold levels and that thresh- old is chosen that minimises the sum-of-squared residuals from the regression, or to put it another way, which maximises R2. Besides of the simple pooled OLS estimation, I additional- ly use panel specific estimations and obtain considerably different results than in the previous literature. Firstly, dividing the sample only into developing and industrial country yields simi- lar results for both groups, where the structural break is determined at 9-13% for industrial countries and 12-17% for developing countries, depending on the estimation technique. Sec- ondly, further division into income groups results in more realistic threshold levels, so that the richest countries show a significant structural break at 2.5-3%, whereas the turning point in the lowest developed countries is between 7-13%.

The rest of the paper is organized as follows. Section 2 compares the different impact of infla- tion on growth in developing and developed countries, whereby the main channels are dis- cussed through which the effect of inflation is manifested. Section 3 presents the literature review of existing empirical evidence about the nature of the nexus between inflation and growth. Section 4 gives a detailed argumentation of the motivation behind this work. Section 5 outlines the theoretical background. Section 6 presents the methodology and data description. Section 7 provides estimation results. Section 8 concludes.

2 Inflation and Economic Growth in Developing vs. Developed Countries

This section explains why inflation rates in developing and developed countries differ consid- erably, but also shows the differences in the impact of a rising inflation. First of all, Dorrance (1963) points out that developing countries are characterised by low and slowly rising in- comes, accompanied by low personal savings. In addition to that, the revenue of the rather poor taxation systems is only enough to cover the basic government services and too little is left for the expansion of the community’s capital or financing development. In order to solve this problem, developing countries may raise the inflation to expand investment and thus easi- ly obtain more capital for a higher growth rate of output. However, with this method only a limited amount of development can be fostered; whereas a moderate monetary expansion, which is slightly greater than the current output growth, will lead to higher savings that are used as resources for development, a too high inflation rate will slow down the development process significantly. A high inflation is hence comparable to high taxation, and may lead to undesirable economic incentives. There may be different channels through which inflation is influencing the growth rate (ibid.). Firstly, high rates of inflation can induce the desire for liquidity in the way that it increases the value of effective liquidity due to the unpredictability of inflation, and thus the uncertainty about the future course of the prices. As a result, both individuals and businesses are holding more liquid assets, rather than investing them. Second- ly, but closely related is the distortive effect of inflation on the price structure, which decreas- es the incentive to save and encourages consumption. In developing countries investment goods are rather imported than produced at home, so a sharp decline in investment leads to relatively large increases in the prices of investment goods. Thirdly, there is evidence that a high inflation leads to balance of payment difficulties, and inflating countries resort to the International Monetary Fund for assistance more frequently than any other country. The main reasons for this are capital flight, higher demand for imports, lower export supplies, as well as large exchange rate depreciations. The rise in imports is due to excess demand for goods, which are purchased from the most readily available elastic source, i.e. imports. With relative- ly higher domestic prices, demand will be diverted to the world economy and away from do- mestic economy. However, trade controls limit this impact of inflation by determining the level of imports. As imports are rising because of higher consumption, a stronger inflation may cause exports to decrease as a result of higher domestic demand. Of course this diversion is limited in an economy with only a few export products. Moreover, higher capital exports than imports increase the balance of payments difficulties on current account. As preventative measures either restrictions on imports or on capital payments may be imposed, or the ex- change rate may be depreciated, which is inevitable if inflation keeps rising. All in all, high rates of inflation can seriously retard growth by discouraging saving, making investment in physical plant and equipment unattractive, and instead encouraging speculative investments in inventories and foreign assets, as well as worsening the balance of payments. And although stabilisation does not automatically lead to development, it is undoubtedly a prerequisite to rapid economic growth.

On the other hand, mild inflation may foster growth. According to Thirlwall and Barton (1971), there are five ways how low rates of inflation can increase economic growth. First, mild demand inflation can be beneficial to keep the resources fully employed so that the sav- ings for investment are maintained on a high level. This in turn keeps production at the full capacity level and increases the real growth. In other words, the well-known Phillips curve applies, which was explained by Kaldor as following: “… a slow and steady rate of inflation provides a most powerful aid to the attainment of a steady rate of economic progress” … “price stability is only consistent with steady growth when the rate of productivity and/or the working population is sufficiently large to give a relatively high rate of growth to the total national product. In a weakly growing economy price stability will mean stagnation unless the propensity to consume is raised sufficiently to offset the effect of a lower rate of growth of profits…”.¹ Second, inflation raises the savings ratio by redistributing from low to high sav- ers. Third, in contrast to high inflation, low and moderate inflation encourages the investment in physical assets, and thus boosting growth through technological progress. The fourth bene- fit of low inflation is that it reduces the real burden of debt and the real interest rate; since interest rates adjust only slowly to inflation, enterprises can benefit from it. Finally, small rates of inflation can help to overcome bottlenecks in the economy more rapidly.

We can see that the manifestation of inflation differs considerably between developing and developed countries. According to this, its effects on economic growth vary from growth promoting, as in industrial countries, to growth impeding, as in the case of developing coun- tries. The aim of this section is to show that if testing for the impact of inflation on growth, countries with a different development level should be analysed separately. Apart from that,the above mentioned mechanisms indicate that low inflation is beneficial for growth, whereas high rates have the opposite effect, which leads again to the research question of this paper, what is the turning point of inflation where the positive relationship turns into a negative? Yet, in former analyses this nonlinear relation was not considered, simply because the results showed an absolutely different pattern comparing to the results from the last two decades. The evolution of research on the inflation-growth nexus was such that initially the data from the decades before 1970 did show neither a negative nor positive effect of inflation. Also further research at the International Monetary Fund could not find any evidence that inflation might be harmful for growth (Sarel, 1996). However, due to the following decades of high and per- sistent inflation in many countries² associated with lower GDP growth, the available data showed changes in the inflation-growth nexus.

3 Literature Review

In the 1990s, a new generation of research on this topic arose. It was univocally confirmed that inflation has a negative impact on growth, and macroeconomic policies are aiming to spur growth by keeping inflation at low levels. This having said, intuitively the question arises, how low should the target inflation be? Or, which is the threshold level of inflation between a positive and negative impact on growth? Many authors in the 1990s attempted to solve this question, with fairly divers results.

Sarel (1996) analyses a panel of 87 countries over the period 1970 to 1990, divided into four five-year averages, and using OLS estimation. He finds a structural break at an average annu- al rate of inflation of 8%. In his estimation model he uses the logarithm of inflation, where he transforms negative inflation rates into small positive, and includes an additional variable,along with other control variables, , with DD being a dummy variable, which is 1 if , and 0 otherwise; the thresh-old level. Finally, he regresses the model with different values for and chooses as the threshold point the which maximises R2, or in other words, the that minimises the sum-of-squared residuals (RSS) (Sarel 1996). Thus he finds that R2is maximised for Below this level, inflation has a positive but weak effect on growth, but for inflation levels above 8%, growth is significantly and strongly negatively affected. Later papers made im- Nonlinear Relation Between Inflation and Growth - Panel Data Analysis, 2013 6 provements towards Sarel’s by dividing the sample in developing and developed countries³, as well as including both negative and positive inflation rates. The justification and rationality of the modifications are explained below in Section 3.

Four years later, Sarel’s methodology was applied on a smaller and more specific sample of countries and years. For 22 East-European transient countries between 1990-1996, Christof- fersen and Doyle (2000) obtained a threshold level of 13%. This was a period of particularly high inflation rates and, at the same time, a sharp decline of output. Unlike Sarel (1996), Christoffersen and Doyle (2000) attempt to also include disinflation in form of dummies. Yet they do not find a significant effect of disinflation on output loss. Furthermore they identify that the output loss related to an inflation rate above the threshold level accounts only for 0.2 percentage points, whereas other studies found this loss to be 1.7 or 0.5 percentage points (see Sarel (1996), Gosh and Phillips (1998)). However, if one assumes that causation runs from inflation to output, the cost of inflation of 0.2 percentage points can be very well understated. Apart from these contributions, their paper also bears some incompleteness. Although their results clearly indicate a threshold level, the confidence intervals are not defined, so that the actual threshold may be higher or lower. Furthermore, no instrument variables were used in order to control for the simultaneity bias, which occurs when one does not take into account that causation can run from growth to inflation through the output gap or other political econ- omy factors (Christoffersen and Doyle, 2000).

The problematic of simultaneity was also taken up by Gosh and Phillips (1998). They state that particularly in a multivariate context, the effect of inflation on growth can be weakened, as other control variables themselves in the regression may be functions of inflation. If in- vestment depends on inflation and growth is affected by investment, then the overall effect of inflation becomes much lower, or even loses its robustness. They approach the analysis of the inflation-growth relationship by employing a panel of all IMF member countries during 1960- 1996 and conducting a panel regression in the first step. In a singlevariate regression growth is positively affected by inflation for very low values. From an inflation rate of 2-3% this rela- tionship changes into a negative and convex one. In the multivariate context they follow Sarel (1996) and use the spline technique to choose a threshold of . In order to allow for the convexity, a simple logarithmic function is used, similar to the one used in Sarel (1996):

[Abbildung in dieser Leseprobe nicht enthalten], where X includes all other control variables (ratios of revenue to GDP, public consumption to GDP, and fiscal bal- ance; openness to international trade, log of the black market exchange rate premium, turns of trade volatility, drought, war-related deaths). The robustness test shows that not allowing for nonlinearity will lead to a downward bias in the inflation-growth slope. It was also argued in the literature that the negative effect of inflation is only due to outliers with very high infla- tion rates, and by dropping these observations from the sample, this relationship can no longer be maintained. Again other studies (see Bruno and Easterly (1998), discussed below) say that only inflation rates of more than 40% have a disastrous effect on growth. Yet, excluding all those observations does not change Gosh and Phillips’ results significantly. Although it is agreed that hyperinflation is bad for economic growth, it is still to be examined whether infla- tion rates of 10-40% have any negative effect on growth. Moreover, they emphasise the im- pact of a potential simultaneity bias on the results, and use different types of IVs with two- stage least squares (2SLS) to control for this. All results with IVs show that previous OLS results are not influenced by a simultaneity bias. However, when using ‘central bank governor turnover rate’ as IV, indeed indicates that the inflation-growth relationship has a growth- inflation channel.

Bruno and Easterly make another approach in their 1998 paper. After noting that inflation does not affect growth in a cross-section analysis, they examine a sample of 31 countries that experienced high-inflation episodes over the period 1961-1994 using a pooled regression. They come up with two major results, which are both contributing to and contradicting the rest of the literature. First, during crisis time, when inflation rates rise to 40% or higher, the relationship is clearly negative and significant. Yet, before and after the crisis, with normal- ised rates, this relationship is strongly positive. Second, while cross-section regression does not reveal any relationship between inflation and growth, the effect of inflation becomes stronger and more negative with high-frequency data and has the strongest impact with annual data. The former result was less accepted in the following literature. Researchers tested Bruno and Easterly’s claim that without high-inflation episodes there is no significant relationship left, and showed that even without hyperinflation observations the negative relationship be- tween inflation and growth remains stable beyond a threshold level. The latter, however, found more acknowledgements among other researchers and it was confirmed that using more frequent data leads to stronger and more robust results.

Motivated by this variety of results, Khan and Senhadji re-examined this issue in their 2001 paper “Threshold Effects in the Relationship Between Inflation and Growth”. They contribute to existing work by extending and modifying their analysis compared to previous literature by, first, looking separately on developing and industrialized countries, and second, by apply- ing new econometric methods, which include the non-linear least squares (NLLS) estimation combined with a hybrid function of inflation, where the threshold level is found with condi- tional least squares. Furthermore, Khan and Senhadji (2001) use the bootstrap method, pro- posed by Hansen (1999), in order to test for statistical significance of the threshold effect. Accordingly, their results differ in so far from previous work as the threshold levels for indus- trialized countries are substantially lower than for developing (1-3% and 11-12%, respective- ly). Furthermore, this result is robust to data frequency, perturbations, and even to exclusion of high-inflation observations, which considerably undermines Bruno and Easterly’s (1998) findings. First major point Khan and Senhadji (2001) make is that growth rates should be re- gressed on the logarithm, instead of the level, of inflation. However, the problem of log trans- formation of inflation rates arises when the rate is less than 1 or even negative, then taking logs is not possible. Unlike Sarel (1996), and later also Burdekin et al. (2004), who convert negative inflation rates into small positive in order to allow log transformation, Khan and Senhadji (2001) adopt the hybrid inflation function of the form:

illustration not visible in this excerpt

The first term is a linear function for values of inflation rates less or equal to one, so that [Abbildung in dieser Leseprobe nicht enthalten] for inflation rates . The second term expresses log of inflation for values above one, such that for inflation rates . By subtracting 1 from the first term, is kept continuous at unity in order to keep it at the turning point from being linear to log linear in . Hence takes into account all inflation rates, posi-tive and negative. In fact, deleting all zero and negative observations, substantially decreases the threshold level, for the reason that not only high inflation is bad for growth but also deflation (Burdekin et al. (2004)). Taking into account the hybrid function (1), Khan and Senhadji (2001) estimate the following model to test for threshold effects:

illustration not visible in this excerpt

where the growth rate of real GDP depends on time and fixed effects; the inflation rate; the threshold level; a dummy ( ), which is one if inflation levels are greater than , and zero otherwise; indicator functions; a vector of control variables; and and showing the effect of inflation on growth for countries with inflation equal or below , and above , respec-tively. The continuity of the relationship described by (2) is maintained. This assumption of continuity at the threshold level is being criticised in the more recent literature (Drukker et al. (2005); Bick (2010)) for two reasons. First, Drukker et al. (2005) argue that small changes in inflation at the threshold level can have different effects depending on whether initial inflation is above or below the threshold. According to Huybens and Smith (1998), non-convexities may lead to a discontinuous drop in per capita growth when inflation increases if initial infla- tion was below the threshold point. The reverse is true when inflation is reduced in a country where the initial level is just above the threshold. Khan and Senhadji (2001) claim that this is only possible when the threshold level is already known, which is not the case in the pre- sent analysis. Consequently, they estimate equation (2) with non-linear least squares (NLLS) after implementing ‘conditional least squares’ (Khan and Senhadji 2001) due to the fact that is not only not known, but also non-linear and non-differentiable. The null hypothesis implies that there are no threshold effects, so that is not identified, and conse-quently classical test have a nonstandard distribution. Following Hansen (1999), Khan and Senhadji (2001) use the bootstrap method to simulate the asymptotic distribution of the likeli-hood ratio test of H0:

However, according to Kremer et al. (2009), applying Hansen’s (1999) method in this context is somewhat problematic. His model requires all regressors to be exogenous, yet the variable initial income is by construction endogenous, as well as inflation, and thus the endogeneity bias may be substantial. Moreover, Bick (2010) points to the fact that the method in Hansen (1999), which is used by Khan and Senhadji (2001) and is explained below, actually implies a discontinuity at the threshold level, and, apart from that, also refers to a balanced panel, which is not given in Khan and Senhadji (2001). Besides testing directly for threshold levels and their significance, Khan and Senhadji (2001) are following Chan and Tsay (1998) and gener- alize the concept of confidence intervals to threshold estimates.

[...]

¹ N. Kaldor, “Economic Growth and the Problem of Inflation“, Economica, August and November 1959; quoted from A. P.

² Sarel (1996): The 1970s and 1980s were characterised by severe and persistent inflation.

³ E.g. Khan and Senhadji (2001), Kremer (2009), Burdekin (2004)