There is a large literature suggesting a robust positive relationship between financial development and economic growth. This view dates back to Schumpeter (1911) who argued that the banking sector plays a key role in economic development, by choosing which firms have the best chance to succeed in the innovation process. The works of Gurley and Shaw (1955), Goldsmith (1969), McKinnon (1973) and Shaw (1973) subscribe to this line. During the last 25 years, by the use of various methodologies, several empirical studies have shown that financial development is not only positively linked to economic growth, but also a good predictor of economic development. Moreover, by increasing intermediation, financial development encourages savings and investment and improves the allocation of savings to investment projects. This in turn leads to high level and great efficiency of capital, which finally stimulates economic growth.1 Although the favourable effect of financial development on growth, only a fewstudies asked whether there are certain conditions that can be associated with a stronger or weaker relationship between the two variables. In this paper, we examine the way in which the finance–growth relationship can vary according to the inflation rate. The variation of this relationship with the inflation rate suggests the existence of non-linearity between both variables and questions the hypothesis made in cross-section and traditional panel data regressions.2 The non-linearity between finance and growth with respect to inflation might be connected to the fact that inflation negatively affects economic growth and thus results in financial repression.

First, several studies report the negative influence of inflation on growth.3 The effects of inflation on the real sector can be either direct or indirect. Inflation increases transactions and information costs, and then impedes efficient resource allocation by obscuring the signals resulting from price changes. In such an environment, characterized by imperfection of the information about prices, economic agents will be reluctant to enter contracts; this penalizes investment and inhibits economic growth. To support this view, Sarel (1996) shows that a structural break exists in the relationship between inflation and growth. According to the author, an inflation rate higher than 8% exerts a powerful negative impact on growth, while for a rate below 8% the impact of inflation tends to be slightly positive. Inflation could be seen as characteristic of underdeveloped economies. Khan and Senhadji (2001) and Khan (2002) also find that the threshold rate of inflation is around 1–3% for industrial countries, while this value ranges between 7 and 11% for developing countries.4 More recently, by using Panel Smooth Threshold Regression (PSTR) on six industrialized countries, Omay and Kan (2010) find that there exists a statistically significant negative relationship between inflation and growth for the inflation rates above the critical threshold level of 2.52%.

Secondly, the financial sector can be hurt by a high level of inflation rate, which can be a consequence or a result of financial repression.5 Indeed, as previously evoked, in an inflationary environment, financial intermediaries dislike long-term financing, which supports growth because of the greater stock return variability and tends to maintain liquid portfolios. Financial intermediaries also dislike higher volatility of inflation rate, because it would make inflation rate less predictable and increase economic uncertainty. In economies with high inflation, intermediaries will lend less and allocate capital less effectively, and equity markets will be smaller and less liquid. Therefore, higher rates of inflation are associated with lower long-run real rates of return on a broad class of assets, and imply more severe rationing of credit, then reducing financial depth. The banking systems hold a significant quantity of non-interest bearing cash reserves in every economy. As is well-understood, higher rates of inflation act like a tax on real balances or bank reserves. And, if this tax is borne, at least in part, by bank depositors, higher inflationmust lead to lower real returns on bank deposits. Since bank deposits compete with a variety of assets, it is plausible that reduced real returns on bank deposits will result in reduced real returns on a variety of assets (Khan, 2002). High price level also encourages the government to implement financial repression policies6 in order to mobilize resources for public spending and to protect certain sectors of the economy. This situation leads to resources misallocation and has harmful effects on economic growth. Furthermore, by increasing the opportunity costs of holding money, inflation causes a lessening of the ratios of money or financial assets to GDP. Khan et al. (2006) and Khan (2002) find that the threshold beyond which inflation significantly hinders financial deepening is estimated to be in the 3–6% range. Boyd et al. (2001) suggest that there is a significant, and economically important, negative relationship between financial development and inflation. Besides, their results support the hypothesis of non-linearity between finance and inflation: for instance, for economies with an inflation rate above 15%, there is a large discrete drop in financial development relative to countries with inflation rate below this threshold.

In spite of the usefulness of the analyses of the relationship between growth and inflation on one side and finance and inflation on the other side, these studies do not allow us to directly conclude with respect to the impact of financial development on the inflation–growth nexus or the impact of inflation on the finance–growth link. Therefore, only a few studies appraise the relationship between inflation, financial development and growth. Rousseau and Wachtel (2002) point out the existence of threshold effects in the finance–growth nexus, by considering the inflation rate for a sample of 84 countries between 1960 and 1995. Their results suggest that the inflation threshold of the finance–growth relationship lies between 13 and 25%.When the inflation rate exceeds the threshold, finance ceases to increase economic growth. More recently, Rousseau and Yilmazkuday (2009) have extended the work of Rousseau and Wachtel (2002) through a trilateral graphic approach and threshold analysis. They find that small increases in the price level seem able to wipe out relatively large effects of financial deepening when the inflation rate lies between 4 and 19%, whereas the finance–growth relationship is less affected by inflation rates above this range. Huang et al. (2010) re-investigate whether there exists an inflation threshold in the finance–growth nexus. Using Caner and Hansen’s (2004) instrumental-variable threshold regression approach to Levine et al.’s (2000) dataset, they find that,when inflation is below8%, financial development impacts growth positively; however, above this critical inflation level, financial development has no statistically significant effect on growth. The threshold identified by Huang et al. (2010) is lower than that of Rousseau andWachtel (2002). Moreover, using a simple panel regression, Giedeman and Compton (2009) find that the positive effect of financial development on economic growth diminishes as inflation increases. Notice that their inflation rate thresholds are unrealistic because they lie between 40% and 80%, according to the financial development variable.

Results suggesting a non-linear relationship between inflation, finance and growth were also obtained by Gillman and Harris (2004) from simple regressions of the growth-containing interaction variable, which is the product of inflation  and financial depth. Nevertheless, Haslag and Koo (1999) find that inflation is never significant in growth regressions that include financial development. Indeed, the results obtained by these authors are surprising as far as the coefficient of the interaction variable (the product between inflation and financial development) is positive.

The main limit of all previous studies consists of assuming that, the relationship between finance and growth can only be affected by cross-country variation of the inflation level, and neglecting inflation change over time. This study fills this gap through the use of Panel Smooth Threshold Regression (PSTR).7

According to Gillman and Harris (2004), and Khan (1999), the channel through which inflation affects growth may run, at least in part, through the financial sector. The topic of this paper is to analyze how the finance-growth nexus is affected by the inflation rate. To do this,we use the methodology of Panel Smooth Threshold Regression (PSTR) developed by Gonzàlez et al. (2005) and Fok et al. (2005). The PSTR model authorizes a smooth transition, for a weak number of thresholds, as well as for a continuum of regimes. This approach presents two main advantages: first of all, a PSTR specification allows the finance-growth coefficient to vary not only between countries, but also in time. This provides a simpleway to appraise the heterogeneous relationship between finance and growth in time and across the countries. Second of all, this approach authorizes a smooth change in country-specific correlation depending on the threshold variables. More specifically in this case,we use the inflation rate as a threshold variable in order to explain the heterogeneity in time and across countries, between financial development and economic growth.

Our results suggest that the relationship between financial development and economic growth is non-linear and this link can be affected by the inflation rate. At the same time, there is an inflation threshold for the finance–growth nexus.  Furthermore, we show that an increase in the price level negatively affects growth through financial developmentwhen the inflation rate is higher than 20%,whereas the impact of finance on growth is positive and significant for an inflation level below 10%.When inflation lies between these two thresholds the finance–growth relationship is positive but very weak.

The rest of the paper is organized as follows. In the next section, we discuss the threshold specification regression. The third part of the paper resumes the main results obtained from the panel threshold estimations. The last section concludes.

1See King and Levine (1993), Beck et al. (2000), Levine et al. (2000), Demetriades and Hussein (1996) and Rousseau and Wachtel (1998) for empirical assessments of the finance–growth relationship. Levine (1997, 2005) also provide a useful survey on the subject.   2The traditional regressions suppose that the finance–growth relationship is linear; it implies that the finance–growth coefficient is constant in time and across countries.   3See Fischer (1993), Barro (1996), Bruno and Easterly (1998) and Hung (2003). Temple (2000) also discusses why inflation should be related to growth and surveys the empirical literature.   4However, using a data set of OECD countries, Andrés et al. (2004) show that, if inflation affects growth through its interaction with financial market conditions, this is not the only channel. They also find that the long-run costs of inflation are not explained by policy of financial repression.   5Although the correlation between inflation and financial repression is established, notice that the causality between both variables remains little documented and can be extended in further studies.   6Financial repression policies can occur by a ceiling interest rate, or by obliging banks to finance governmental projects.   7Notice that inflation is not the only source of non-linearity between finance and growth. This nonlinear relationship can also depend on structural parameters as well as on variables of economic  policies. For more details see Berthélemy and Varoudakis (1995, 1996), Aghion et al. (2005), Deidda and Fattouh (2002, 2008), Gaytan and Rancière (2004), Ketteni et al. (2007), and Huang and Lin (2009).

The basis of our model is exactly the same as the one used by many authors who investigate the finance–growth relationship on panel data. The corresponding equation is then defined as follows:

where g_it is the GDP growth rate observed for the ith country at time t, f_i,t−1 is the first lag of the financial development indicator,8 α_i denotes an individual fixed effect, z_it a vector of control variables.9 The residual ε_it is assumed to be i.i.d.

This model, which is used for the first empirical estimations of the finance–growth relationship, presents two main drawbacks. First, it supposes that the finance-growth coefficient remains for all the countries of the sample. Second,  this model implies that the finance-growth coefficient is constant in time. It seems unrealistic as the effect of financial development on growth at the beginning of the 1960s might be different from its effect in the 2000s. To solve these problems, we can suppose that the panel is heterogeneous and consequently parameter (β_i) is a random coefficient (random coefficient model of Swamy, 1970). However, this method also reveals its limits as far as it only takes into account the difference of the elasticity between the countries, and hides the variability of the parameter with time.

One solution to circumvent both these issues consists of introducing threshold effects in a linear panel model. In this context, the first solution requires using the Panel Threshold Regression (PTR) model (Hansen, 1999) as suggested by Deidda and Fattouh (2002). In this case, the mechanism of transition proposed by Hansen (1999) between extreme regimes is very simple: at each date, if for a given country, the transition variable is lower than a given value, called the threshold parameter (which is in our case the inflation rate), then the finance–growth model is defined by a particular regime, and this regime is different from the model used if the transition variable is larger than the threshold parameter. For instance, let us consider a PTR model with two extreme regimes:

where q_it (q_it = Infl_it, the inflation rate) is the threshold variable, c a threshold parameter and the transition function Γ(q_it, c) corresponds to the indicator function:

with such a model, the finance-growth coefficient is equal to (β₀) if the threshold variable is smaller than c (qit < c), and is equal to (β₀ + β₁) if the threshold variable is larger than c (q_it ≥ c). This model can be extended to a more general specification with r regimes. However, even in this case, the PTR model imposes that the value of the finance–growth coefficient can be divided into a small number of classes. Such an assumption is unrealistic for a sample of developed and developing countries. Because a model with a few thresholds seems to be simple way to assess finance–growth linkage, one can assume that the consideration of an infinite number of thresholds could be a possible solution.

The conventional solution to this problem is the use of a model with a smooth transition function. This type of model, commonly used in time series analysis, has recently been extended to panel data with the Panel SmoothThresholdRegression (PSTR) model proposed by Gonzàlez et al. (2005) and Fok et al. (2005). Let us consider then the simplest case of a PSTR with two extreme regimes and a single transition function to illustrate the relationship between finance and growth:

The transition function Γ is continuous and depends on the threshold variable q_it; c = (c₁, . . . , c_m)´ is a vector of parameters and the parameter γ determines the slope of the transition function. Following thework of Granger andTeräsvirta (1993) for time series STAR models, González et al. (2005) used a logistic transition function:

The main advantage of PSTR is that it allows the finance-growth coefficient to vary according to the country and in the time dimension; hence it provides a parametric approach of cross-country heterogeneity and of time instability of the finance-growth coefficients, since these parameters change smoothly as a function of a threshold variable,which in our case is the inflation rate. The finance–growth coefficient for the ith country at time t is defined as follows:

According to the properties of the transition function, we have β₀ ≤ e_it ≤ β₀ + β₁ if β₁ > 0 or β₀ + β₁ ≤ e_it ≤ β₀ if β₁ < 0 because 0 ≤ Γ(q_it; γ , c) ≤ 1. We notice that the finance–growth coefficient can be defined as aweighted average of parameters β₀ and β₁. Then, the PSTR model allows a precious assessment of the impact of finance on growth with inflation.

Another advantage of the PSTR model is that the finance–growth coefficient may be different from the estimated parameters for extreme regimes, i.e. β₀ and β₁. As illustrated by equation (6), these parameters do not correspond to the direct impact of financial development on growth. For instance, parameter β₀ corresponds to the direct effect of finance on growth only when the transition function Γ(q_it; γ , c) tends towards 0. On the contrary, when Γ(q_it; γ , c) tends towards 1, the finance-growth coefficients is equal to the sum of β₀ and β₁ parameters. Between these two extremes, there are an infinite number of finance-growth coefficients, which are defined as a weighted average of parameters β₀ and β₁. Therefore, it is suitable to interpret (i) the sign of these parameters, which indicates an increase or a decrease of the finance–growth coefficient depending on the value of the inflation rate; and (ii) the varying coefficient in the time and individual dimensions given by equation (6).

Although these expressions of the elasticity allow some configurations for the finance and growth relationship, several questions relative to estimation and specification tests persist. The next section is devoted to answering them.10

The PSTR model estimation consists of several stages. It begins by removing individual-specific means and then by applying non-linear least squares to the transformed model.11 Then, we use the following testing procedure: first, the linear against the PSTR model is tested,12 and, second, the number r of transition functions is determined. Testing the linearity in a PSTR model (equation (4)) can be done by testing: H₀: γ = 0 or H₀: β1 = 0. In both cases, the test is nonstandard since the PSTR model contains unidentified nuisance parameters under H₀. A possible solution is to replace the transition function Γ(q_it; γ , c) by its first-order Taylor expression around γ = 0, and to test an equivalent hypothesis in an auxiliary regression. We then obtain:

Since θ_i parameters are proportional to the slope parameter of transition function γ , testing the linearity of finance-growth model against PSTR consists of testing: H₀: θ₁ = 0 versus H₁: θ₁ ≠ 0. Let us denote by SSR₀ the panel sum of squared residuals under H₀, and SSR₁, the PSTR model with two regimes. The corresponding F−statistic is then defined by:

where T is the number of years, N the number of countries, and K the number of exogenous variables.

Once the linearity test is used, the problem is to identify the number of transition functions in the model.The sequential approach by testing the null hypothesis of no remaining non-linearity is generally used. If the linearity hypothesis has been rejected, the issue is then to test whether there is one transition function (H₀: r = 1), or whether there are at least two transition functions (H₁: r = 2). Let us suppose a model with two transition functions (r = 2), defined as:

Γ₁(q_it; γ₁, c₁) and Γ₂(q_it; γ₂, c₂) are two different transition functions. The procedure of the test consists of replacing the second transition function by its first-order Taylor expression around γ₂ = 0, and then in testing the linear  constraints on the parameters. The model becomes:

The test of no remaining non-linearity is simply defined by: H₀: θ₁ = 0. Again, a LM_F test is used with SSR₀ the panel sum of squared residuals under H₀, i.e. in a PSTR model with one transition function and SSR1 the sum of squared residuals of the transformed model (equation 10).

Then, the testing procedure is as follows. Given a PSTR with r = r^∗ transition functions, we test the null hypothesis H₀: r = r^∗ against H₁: r = r^∗ + 1. If H₀ is not rejected, the procedure ends. Otherwise, the null hypothesis H₀: r = r^∗ + 1 is tested against H₁: r = r^∗ + 2. The testing procedure continues until the first acceptance of H₀. Given the sequential aspect of this testing procedure, at each step of the procedure the significance levelmust be reduced by a constant factor τ , such as 0 < ρ < 1, in order to avoid excessively large models. We assume ρ = 0.5 as suggested by González et al. (2005).

8We use the lag of the financial development variable to treat the endogeneity problem between financial development and economic growth.   9See next section (data and threshold results) for more details.   10For the analysis of the asymptotic behaviour of the PSTR estimator, see González et al. (2005) and Fok et al. (2005).   11See Gonzàlez et al. (2005) and Colletaz and Hurlin (2006) for more details.   12We assume in our specification that the transition functions have one threshold. If some models require transition functions with more than one threshold, we may use in these cases several  functions with one threshold.

This study is based on a selection of 71 developed and developing countries,13 over the period 1960–2004. Our data are taken from PennWorld Tables (PWT 6.2) and from the financial database realized by Beck et al. (1999), updated in 2005. The financial development is measured by three variables in order to capture the variety of the different channels throughwhich finance can affect growth:14 BANKequals the ratio of commercial bank assets divided by commercial plus central bank assets. This variable measures the degree to which commercial banks allocate society’s savings versus the central bank. DEPOSIT is calculated by dividing deposit money bank assets to GDP, and the last financial indicator is PRIVATE, which equals the value of credits by financial intermediaries to the private sector divided by GDP. This measure of financial development is more than a simple measure of financial sector size. PRIVATE isolates credit issued to the private sector, as opposed to credit issued to governments, government agencies, public enterprises and the central bank. The endogenous variable is the Gross Domestic Product (GDP) per capita in PPP (constant price 2000 in US dollars). Following the works of Levine et al. (2000) and Beck et al. (2000), we use a set of variables that controls for other factors associated with economic growth and for the assessment of the strength of an independent link between financial development and growth. We use the inflation rate and the ratio of government expenditure to GDP as indicators of macroeconomic stability, and the sum of exports and imports as a share of GDP to capture the degree of openness of an economy. Finally, the population growth rate (POP) allows us to appraise the impact of population dynamics on growth.We can point out that inflation rate is also used in transition functions. As recommended by Hansen (1999), we consider a balanced panel. Table 1 presents different properties of the variables we used.

We consider three different models (Model A, B and C) according to the financial development indicator. For each model, the first step is to test the linear specification of economic growth versus a specification with threshold effects.  If the linearity hypothesis is rejected, the second step will be to determine the number of transition functions required to capture the non-linearity. We make the assumption that in our PSTR model, a single location parameter is used in  the logistic transition function (i.e. m = 1).15

The results of these linearity tests are reported in Table 2. For each model (indicator of financial development), we compute the statistics for the linearity tests LM_F (H₀: r = 0 versus H₁: r = 1) and for the tests of no remaining nonlinearity LM_F (H₀: r = a versusH₁: r = a + 1, for a not equal to 0). The values of the statistics are reported up to the non-rejection ofH₀. The LM_F tests lead clearly to the rejection of the null hypothesis of linearity between financial development and economic growth, by using inflation rate as a threshold variable.Whatever the financial development variable, the linearity test (H₀: r = 0) is strongly rejected according to the LM_F statistics. This result confirms the non-linear relationship between finance and growthwhen accounting for inflation as a threshold variable, whichwas highlighted in the previous literature and documented by Rousseau and Wachtel (2002) and Gillman and Harris (2004).

The specification tests of remaining non-linearity led also to the identification of the optimal number of transition functions or extreme regimes. As reported in Table 2, for all three tests, the null hypothesis of the remaining non-linearity cannot be rejected for r = 2; this suggests that the optimal number of transition functions is two. In other words, cross-country and time heterogeneity between financial development and economic growth according to the inflation rate can be captured through a PSTR model with two transition functions (or three extreme regimes). However, notice that, PSTR models with two extreme regimes (r = 1) can be considered as a model with an infinite number of intermediate regimes.The finance–growth coefficients are defined for each country at each date as weighted averages of the values obtained in the three extreme regimes. These weights rely upon the value of the transition function, which depends on the inflation rate. So, even if we have three extreme regimes, this model allows a ‘continuum’ of coefficient values, each one associated with a different value between 0 and 1 of the transition function Γ(.).

The specification of the estimated equation for the final PSTR model is the following:16

Table 3 contains the parameter estimates of the final PSTR model (with two transition functions). The control variables have the expected signs: the inflation rate, the ratio of government expenditure to GDP and the openness to trade have a significant negative impact on economic growth,while the effect of the population rate is not significant.

We note that the estimated values of the slope parameters γ_j are relatively high (for instance 411.3 and 202.7 for the first and the second transition function respectively in Model A; the same results are obtained for models B and C). Recall that when the slope parameter tends to infinity, the transition function tends to an indicator function. Consequently, the transition functions are quite sharp and the non-linearity between finance and growth with respect to the inflation rate is close to a three-regime PTR model. So, this non-linear relationship can be appraised through two PTR models. As regards the location parameters c_j, they indicate the inflation level at which the transition function reaches an inflexion point. The results are quite similar for the three models. The first inflexion point is obtained for an inflation rate between 9.49 and 15.99, and the second inflexion point corresponds to an inflation rate between 19.34 and 25.62.

As mentioned above, the estimated parameters β_j cannot be directly interpreted, but their signs are. For instance, ifwe consider PSTR model for all financial development variables (r = 2), the parameter β₀ is always positive, whereas the coefficients β₁ and β₂ are negative. This implies that when the threshold variable (i.e. inflation rate) increases, the link between economic growth and financial development decreases. Given the sign of the parameters β₁ and β₂, our model confirms that the finance–growth coefficient will lessen with a higher level of inflation. Following an increase in the level of inflation, the relationship between financial development and economic growth declines in two stages. However, the main advantage compared with previous studies is that our model permits us to assess the relative quantitative impact of the inflation rate on the finance–growth nexus; it provides newproof of the existence ofmultiple balances between finance and growth, which can also depend on the inflation rate. Thus, according to its inflation rate, a country can reach different equilibrium. As the model accepts two transition functions, which are quite sharp (i.e. three balances), for a low level of inflation rate (lower than the first threshold), the finance–growth coefficient is β₀, whereas for inflation rates between the first and the second threshold this coefficient is β₀ + β₁. Notice that β₀ + β₁ is lower than β₀ because β₁ < 0; the transition function in this case is an indicator function. Indeed, for high inflation (i.e. higher than the second threshold) the relationship between finance and growth is given by the coefficient β₀ + β₁ + β₂. These outcomes highlight a decreasing relationship between the impact of financial development on growth and the inflation rate.

Then, our results suggest that for the low level of inflation rate the financegrowth coefficient lies between 1.183 and 1.837. For an inflation rate lying between 9.494% and 24.620%, the finance-growth coefficient is 1.115, 0.637 and 0.464 for BANK, DEPOSIT and PRIVATE, respectively. By contrast, for a high level of inflation (i.e. higher than the last threshold), the sensitivity of growth to finance is 0.147, 0.068 and −0.563 respectively for BANK, DEPOSIT and PRIVATE.17 The decline of the finance–growth coefficient shows that a macroeconomic environment characterized by a high level of inflation is less convenient for a favourable impact of financial development on growth.

For a better illustration of the impact of the inflation level on the finance–growth relationship, Figure 1 depicts the elasticity defined by equation (6) against the inflation rate, and derives three balances for all models. Furthermore, Model A shows that for an inflation level less than 9%, the finance–growth coefficient is close to 1.84; this value is near1%for an inflation rate between 9 and 20%. Indeed, beyond an inflation threshold of 20%, economic growth is no longer sensitive to financial development. The same conclusion can be drawn fromthe other models with a slight change in the thresholds and the finance–growth coefficients. This suggests the robustness of our results to various financial development indicators.

Our results are similar to those obtained by Rousseau and Wachtel (2002). However, our results allow for more debate assessment of the implications of the inflation on the finance–growth relationship: three equilibria are identified  according to inflation rate; that is not the case in Rousseau and Wachtel’s paper.

Overall, the estimation of the non-linear relationship between finance and growth with respect to the inflation rate highlights that, in countries that record high inflation, economic growth is less sensitive to financial development. Therefore,  an economic policy that aims to increase the sensibility of growth to finance will control and fight inflation.

13The sample is the following: 18 low-income countries (Burkina Faso, Burundi, Ivory Coast, Ethiopia, Gambia, Ghana, Haiti, India, Kenya, Madagascar, Nepal, Niger, Nigeria, Pakistan, Rwanda, Senegal, Sierra Leone, Togo); 30 middle-income countries (South Africa, Argentina, Barbados, Bolivia, Chile, Colombia, Costa Rica, Egypt, El Salvador, Ecuador, Gabon, Guatemala, Honduras, Iran, Jamaica, Malaysia, Morocco, Mauritius, Panama, Dominican Republic, Paraguay, Peru, Philippines, Seychelles, Sri Lanka, Syria,Thailand,Trinidad andTobago, Uruguay,Venezuela); 23 high-income countries (Australia,Austria, Belgium, Canada, Cyprus, Denmark, Finland, France, the UK, Greece, Iceland, Ireland, Israel, Italy, Japan, Norway, New Zealand, the Netherlands, Portugal,  Singapore, Sweden, Switzerland, the USA). The countries are selected according to the data availability.   14Financial development is measured only through banking sector indicators. We don’t use in this paper stock market indices, given that these variables are only available for developed countries.   15However, in the case of a model with at most one threshold for each transition function, Colletaz and Hurlin (2006) suggest the use of the testing procedure proposed by Granger and Teräsvirta (1993) which can be adapted in the case of PSTR models so as to choose between m = 1 and m = 2. Except for this special case, there is no general specification test for the choice of m.   16A positive correlation between financial development and growth variables in this paper means that financial development has a positive effect on economic growth. I would like to thank the  referee for this suggestion.   17These values are derived from the derivation of the PSTR growth equation (equation (11)) and are highlighted in Figure 1.

The recent empirical literature has shown that the relationship between financial development and economic growth is mostly positive, and significant. However, the impact of the inflation rate on this link is not often questioned in the literature. This paper helps to shed light on the complex interaction between financial development, inflation rate and economic growth, using the methodology of Panel Smooth Threshold Regression (PSTR) developed by Gonzàlez et al. (2005). So, this study proposes an original framework to appraise the non-linear relationship between financial development and growth with respect to the inflation rate. Our findings confirmthe non-linear pattern of this relationship and its dependence on inflation. More exactly, this non-linearity can be estimated through three extreme regimes. The evolution of inflation effects on the finance–growth link shows that: for an inflation rate lower than 10 to 15% (according to the financial development variable), the positive effect on growth is between 1.18% and 1.84%; this suggests that disinflation is associated with a strong positive effect of finance on growth. The impact of finance on growth lies between 0.5% and 1%, for a level of inflation between 10 and 24%. Indeed, the threshold level of inflation beyond which inflation significantly hinders the finance–growth relationship is estimated to be in the 20–24% range. These outcomes confirm the empirical assessments of Rousseau and Wachtel (2002) and Rousseau and Yilmazkuday (2009).

Our results highlight serious macroeconomic consequences of not avoiding excessive inflation on economic growth. These results provide strong empirical confirmations of the economic policy, which recommends low inflation for a  strong relationship between the financial and real sectors.The policy implications derived from these findings consist of the development of institutional arrangements for controlling and fighting inflation, for maintaining macroeconomic  stability, and for encouraging the real impact of financial policy on economic growth.