The Non-Linear Relationship Between Inflation

and Economic Growth in Mexico

and Economic Growth in Mexico

Date received: February 5, 2013. Date accepted: August 13, 2013

Abstract

This article aims to study the effect of prices on economic growth in Mexico during the time of the inflation objectives model. The analysis is based on modeling the nonlinear relationship between inflation and the product of three economic activities in the country, using three types of panel data estimators (constant, fixed and random). The results reveal that the effect of inflation on the products of sectors has gradually fallen as price levels have decreased, in accordance with the central bank adopting inflation objectives.

Keywords: Mexico, inflation, prices, sector products, monetary policy.

INTRODUCTION

The origins of the current macroeconomic^{1} consensus governing price control can be found in New Zealand, where, in 1990, the country's central bank adopted an inflation targeting regime as its monetary policy.^{2} The inflation targets model rests on the idea that a central autonomous bank, able to use the interest rate as a monetary policy tool, can achieve price stability^{3} through a quantitative inflation target (without producing economic growth or expansion) (Taylor, 1993, 1998).^{4} In this novel paradigm, monetary policy is a fundamental tool to achieve macroeconomic balance (Layard, 1998: xi), where price control, rather than any other economic policy^{5} objective, is the primary mission of central banks (Bernanke and Mishkin, 1997: 3-4; Mishkin, 2000: 2-4).^{6}

In Mexico, where the Bank of Mexico has constitutional autonomy and there is a free floating exchange rate,^{7} in January 1999, an inflation target of 13 percent was adopted for the first time (Martínez *et al.*, 2001: 8), which was the case until 2002, when the target was adjusted to its current 3 +/- 1 percent.^{8} Price control has become the central mission of the Bank of Mexico,^{9} backed by the idea that stable price levels are the best and only contribution that monetary policy can make to long-term economic growth (Bernanke *et al.*, 1999; Woodford, 2003).^{10} In this context, this research focuses on modeling the effect of the current monetary regime on the economic growth^{11} of Mexico, and more specifically, on the product of primary, secondary and tertiary activities in the Mexican economy.

Empirically speaking, various panel data^{12} estimators were used to conclude that the current monetary scheme has indeed benefitted economic growth in the country. Using an aggregate demand function where inflation for three activities is inversely related with their product, when inflation is controlled by quantitative targets, the non-linear relationship between the two variables is reduced.^{13} Consequently, even though economic growth is not the objective of monetary policy in the country, when the effect of inflation on the product of three economic sectors is reduced, the inflation targeting monetary regime has an *indirect* benefit on real macroeconomic growth.

Finally, this work is structured as follows. The section on the inflation targets model also describes the theoretical framework of this research. The model proposal outlines the terms of a panel data econometric model, which will be used in this study. The econometric estimates are described with the empirical evidence of this work. The conclusions section analyzes the principal contributions of this research, ending with a statistical appendix and the bibliography and references.

THE INFLATION TARGETING MODEL

In keeping with conventional monetary policy, the theoretical functioning of the inflation targeting model exists in the relationship between the following equations:

Taylor Rule (1) | |

is Curve (2) | |

Phillips Curve (3) |

Where is the real interest rate, is the natural interest rate,^{14}
the difference between observed inflation and the inflation target the difference between the effective and potential product disturbances of aggregate demand in the is curve,^{15} the observed inflation in a period, the disturbances in prices in the Phillips curve, and the coefficients and are parameters that measure the sensitivity of dependent variables on independent variables.^{16}

The three above equations were used to build an aggregate supply and demand model that explains the theoretical functioning of the inflation targeting scheme in an economy like the Mexican economy.^{17} To build the demand curve, use equation (1) (without the product gap),^{18} and equalize with respect to and :

(4) |

As (4) only depends on the inflation gap, when this term is equalized with the is equation curve (2), the following aggregate demand curve results:

(2) |

Where is directly dependent on disturbances in demand () and indirectly on the inflation gap () (Hicks, 1937; Taylor, 1998).^{19}

With the demand curve in place, it was time to build the supply curve, using logical reasoning with respect to the Phillips curve. If a conventional aggregate supply curve describes the total amount of goods and services that companies are willing to sell at a determined price level, this same reasoning can be found in the Phillips curve for equation (3), where the term is replaced by , producing the following curve.

(6) |

With (6), the expectations of individuals are no longer adaptive and become rational, when the inflationary prospects of companies are fixed through the expected inflation rate in the entire economy (and not on past behavior) (Friedman, 1968; Phelps, 1968).

With the aggregate supply and demand curves, the steady state inflation targeting model is as follows:

Figure 1. Aggregate Supply and Demand Curves

Source: Prepared by the author based on Jones 2009).

Here, the slope of the aggregate demand curve is negative, due to the inverse relationship between the real interest rate and economic production (is curve) (Hicks, 1937), while the aggregate supply curve has a positive slope, due to the direct relationship between production and inflation (Phillips curve) (Friedman, 1968; Phelps, 1968). Moreover, the intersection point of the curves indicates that expected inflation and effective production are equal to the inflation target and potential production, so in these conditions, the economy is in a long-term equilibrium (see Figure 1).^{20}

Operationally, the setting inflation targets in an economy like the Mexican economy can be understood with the following example: assuming that a central bank^{21} decides to go from inflation of 4p to an inflation target of 2p,^{22} aggregate demand will go from AD to AD', situating the economy in point B with a lower product than in point A (see Figure 2):

Figure 2. Inflation Targeting Model

Source: Prepared by the author based on Jones (2009).

However, similar to how in equation (6) we went from a Phillips curve with *adaptive expectations* to an aggregate supply (AS) curve with *rational expectations*, when the economy goes from 4p to 2p, economic agents adjust their inflationary prospects to the new target^{23} (meaning that AS falls to AS’).^{24} With this adjustment, the AD’ and AS’ curves find equilibrium in point C with the same product level as before the inflation target was implemented (see Figure 2),^{25} which acknowledges that monetary policy is a nominal anchor for the economy (Layard, 1998: xi).^{26}

Said another way, the function in Figure 2 predominates in the traditional form of the Taylor rule, because when the product gap increases , inflation and its gap do as well .^{27} As such, according to Taylor, central banks should increase their real interest rate until both relationships are fulfilled and , a point at which the economy reaches price stability (Taylor, 1998).^{28} However, because central banks cannot control the real interest rate (Blinder, 1998: 33), they must increase the nominal (short-term) interest rate by a proportion greater than the growth of the inflation rate (Taylor, 1993), until (Perrotini, 2007: 66-71).^{29}

Finally, although the canonic version of the model does not include the exchange rate as a relevant variable in price control, some versions do. For example, Lars Svensson, Laurence Ball and, most recently, Philip Arestis, find that price control is not achieved entirely through the interest rate, but rather through a monetary price index that includes the exchange rate as merely another tool (Ball, 1998: 3-4; Arestis, 2009: 4-8). Even so, because the entire theoretical foundation of this work is based off the original structure of the model, we shall assume that the interest rate is the primary monetary policy tool (Taylor, 1993, 1998: Bernanke *et al.*, 1999; Woodford, 2003). Because Mexico's exchange rate has been free floating, its effect on price levels has fallen in recent years (pass-through effect) (Baqueiro *et al.*, 2003; Capistrán *et al.*, 2011; Pérez, 2012b; Cortés, 2013).

APPROACHING THE PROBLEM

To model the effect of the inflationary targets model monetary regime on the product of primary, secondary and tertiary activities in Mexico, using the aggregate demand curve from equation (5),^{30} the goal of this research in terms of a panel data model^{31} is as follows:

(7) |

Where the subscript *i* corresponds to the three economic activities in the country, *t* to the period of study,
is the system constant, is the parameter to estimate,^{32} and is the error term representing the observed variation of that cannot be explained by the observed variation in (Pérez, 2006: 679).

To model equation (7), in terms of the real economic reality of Mexico, its variables must be replaced by observable units of measure.^{33} The product cap was replaced by the global economic activity index (igae) for each sector.^{34} The inflation gap was replaced by inflation for spending^{35} on the various types of goods and services that make up each activity.^{36} Likewise, so that the inflation effect on igae can be read in percentage terms, both variables were transformed into their natural logarithm (Ln), and the equation was as follows:

(8) |

Here, the only parameters to estimate are the constant (disturbances in aggregate demand in the is curve), and the coefficient (which measures the sensitivity of inflation to economic production).^{37}

In terms of the period of study, although the first time that inflation targets were implemented in the country was in 1999,^{38} this research focuses on the time period starting with the launch of the free floating exchange rate^{39} (*sine qua non* condition of the model), to nearly the present (1995: January/April, 2013). In the period prior, because there is a distinction between one and two digit inflation (measured by the change in the ncpi),^{40} in the fourth month of 2000, this break appears (see Figure 1).

Consequently, by dividing the periods into 1995: January/March 2000 and 2000: April/April 2013, we can make two econometric estimates using equation (8), which helps to understand the effect of inflation on sectoral production before and during the current monetary regime.^{41} With this, although the initial goal was to evaluate the non-linear relationship between the two variables, on a second level, we could also analyze the effectiveness of this monetary scheme by comparing these results with those of its closest homologue^{42} (in this case, the “corto” policies of the Bank of Mexico [Martínez, *et al.*, 2001: 4-16]).^{43}

Figure 1. National Consumer Price Index, 1995: January/April 2013

Source: Prepared by the author based on inegi data.

ECONOMETRIC ESTIMATES

With the specifications described in the above section, the estimated results for constant, fixed and random effects under the (standard) ordinary least squares (ols) method,^{44} are as follows:

Where the estimated parameters of the six regressions are statistically significant at 99 percent confidence. With respect to the type of estimators to include, using the *Fixed-effects* and *Hausman fixed* tests, Table 1 rejects the null hypothesis that the coefficients are fixed (and accepts the estimators due to constant or random effects) and Table 2 rejects the null hypothesis that the coefficients are constant and fixed (and accepts estimators due to random effects).^{45}

By choosing the estimators due to random effects, the economic analysis in the previous tables can summarized in the following equations:^{46}

(9) |

(10) |

Where an increase in inflation by one percentage point, means a loss of igae in the non-inflationary targets period of 0.10 percent (9), while the loss for the inflationary targets period is merely 0.05 percent (10).^{47} Consequently, although it is practically impossible to evaluate a variable with respect to another (or others), what is important here is not to strictly estimate the effect of inflation on igae, but rather to compare their relationship between two periods with different monetary schemes in place.^{48}

The increase of national igae, given by a reduction in prices in the three economic activities, is shown in Figure 2.

In this graph, economic growth is higher when prices fall, in other words, during the current regime.^{49} Therefore, the above empirical analysis corroborates the idea that even though there is a non-linear (and intrinsic)^{50} relationship between the two variables, when prices are low and stable, there is loss product loss when these variables increase (which follows the central bank adopting inflationary targets).^{51}

Figure 2. National igae and inflation: 1995-2013

Source: Prepared by the author based on in inegi data.

Finally, something else to consider, in addition to the above, is to compare the fulfillment of inflationary targets with national igae growth rates:

The above data shows that since 2002, when inflationary targets began, they have only been met 42 percent of the time. With the product behavior, the igae growth rate from 1995-2001 was 2.54 percent, slightly higher than the 2.14 percent in the period 2002-2013. Consequently, in a context of low economic productivity, maintaining low and stable inflation may be an advantage that stimulates the Mexican economy in the long term, without losing sight of the fact that price stability is just one factor in the national economic agenda.

CONCLUSIONS

In 1970, the end of the Bretton Woods system and the opec oil crises played host to an abnormal combination of production stagnation and high inflation (stagflation) (Krugman and Obstfeld, 2006: 572), which upended the entire organization and functioning of the international system (Block, 1977). To achieve desired stability, monetary policy became a fundamental tool to acquire macroeconomic balance (Layard, 1998: XI), making price control, rather than any other economic policy objective, the primary mission of central banks (Bernanke and Mishkin, 1997: 3-4; Mishkin, 2000: 2-4). In this context, this work has set out to study the implications of the economic growth that has accompanied the current monetary scheme, which in terms of this research can be summarized in the following points:

- Based on the panel data model econometric estimates of constant, fixed and random effects, the non-linear relationship between inflation and the product of three economic activities in Mexico fell from April 2000-April 2013 (which matches the time when the central bank adopted inflationary targets).
- Although constitutionally, the sole mission of the Bank of Mexico is price control, this has had an
*indirect*benefit on real macroeconomic growth, because when the non-linear relationship between these two variables decreases, losses in the product (in the presence of price increases) fall in comparison with previous years. - Finally, with a national igae growth rate of 2.14 percent during the time period of inflationary targets (lower than the 2.54 percent of the previous period), it was demonstrated that maintaining low and stable inflation may be an advantage that stimulates the Mexican economy in the long run (as long as price reductions do not represent a sacrifice in national production).

Generally speaking, the inflationary targets model has generated an environment of stability for the Mexican economy. By setting inflation expectations for economic agents (Phillips curve), the non-linear relationship between inflation and the product has fallen (is curve). Consequently, based on the Bank of Mexico’s parsimonious following of its reaction function (Taylor rule) (Pérez, 2012a), it could be said that current price controls are a monetary policy measure that supports long-term economic growth. Even so, although this analysis avoids some criticisms that have been made of the model (*i.e.*, the transfer of the exchange rate to prices, fear of a free floating currency, sterilization in the currency market, etc.),^{52} this does not make this research any less important. The results presented here should only be taken as true in the context of the theoretical and methodological criteria under which they were constructed.

STATISTICAL APPENDIX

Figure 1. Primary Activities, 1995-2013

Source: Prepared by the author based on inegi data.

Figure 2. Secondary Activities, 1995-2013

Source: Prepared by the author based on inegi data.

Figure 3. Tertiary Activities, 1995-2013

Source: Prepared by the author based on inegi data.

Figure 4. igae and inflation for Primary Activities, 1995-2013

Source: Prepared by the author based on inegi data.

Figure 5. igae and inflation for Secondary Activities, 1995-2013

Source: Prepared by the author based on inegi data.

Figure 6. igae and inflation for Tertiary Activities, 1995-2013

Source: Prepared by the author based on inegi data.

Figure 7. Cycle of Primary Activities, 1995-2013

Source: Prepared by the author based on inegi data.

Figure 8. Cycle of Secondary Activities, 1995-2013

Source: Prepared by the author based on inegi data.

Figure 9. Cycle of Tertiary Activities, 1995-2013

Source: Prepared by the author based on inegi data.

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^{*} Graduate of the UNAM Faculty of Economics, Mexico (this article is part of a thesis to obtain a Bachelor's degree in Economics). laurrabaquio@comunidad.unam.mx

^{1} The term *consensus*, from Arestis, refers to rather low agreement among economists of the traditional persuasion, because, starting with the is-lm model at the end of 1960, there really has been no consensus with regards to macro-level themes that prevailed with the neoclassical synthesis.

^{2} See www.rbnz.govt.nz/monetary_policy/policy_targets_agreement/0073109.html

^{3} “Price stability [is understood] as a situation in which families and companies can safely disregard the risk of widespread and sustained price increases or decreases when making savings and investment choices" (Angeriz and Arestis, 2009: 22).

^{4} Strictly speaking, the pillars of this model find their origin in the Swedish economist Knut Wicksell, who applied the central banking system of his country in the 1920s with a monetary (Wicksellian) scheme that sought price stability through a discount interest rate (Wicksell, 1898).

^{5} Intermediate goals (like growth of monetary aggregates, exchange rate control, etc.) do not play a relevant role in the model (Bernanke and Mishkin, 1997).

^{6} In the words of Frederic Mishkin, in the inflation targets regime, “price stability is the primary goal of monetary policy, to which other goals are subordinated” (Mishkin, 2000: 1).

^{7} The free floating exchange rate is a *sine qua non* condition of the model, as it helps the central bank meet its desired inflation target, without distracting from monetary policy in combating a financial crisis (Perrotini, 2007: 72-73).

^{8} The inflation target in Mexico is measured by the change in the national consumer price index (ncpi) (see www.banxico.org.mx/divulgacion/politica-monetaria-e-inflacion/politica-monetaria-inflacion.html#Esquemadeobjetivosdeinflacion).

^{9} Sixth paragraph of Article 28 of the *Political Constitution of the United Mexican States*, or Article 2 of Chapter 1 of the *Law of the Bank of Mexico*.

^{10} See Bernanke and Mishkin (1997: 30), Sterne (2001: appendix) and Roger (2010: 47) for a compilation of countries that have adopted an inflation targets plan.

^{11} Unless otherwise specified, *economic growth* is a function of the product, and not of income.

^{12} This work has opted for a panel data model, rather than a time series model, because this allows us to analyze the behavior of prices through each of the components of overall inflation in the same regression (which will provide more consistent results when evaluating the benefits of the current monetary scheme).

^{13} The relationship between inflation and product falls during the inflation targets period, when compared to estimates of the previous monetary regime (in this case, the accumulated balance policies of the Bank of Mexico, also known as the “corto” regime).

^{14} The real interest rate is the nominal interest rate minus the expected inflation rate (Hall and Taylor, 1992: 201), while the natural interest rate is the marginal product of capital, that is, the additional quantity of production obtained when an additional unit of capital is invested, maintaining the amount of labor constant (Mankiw, 2007: 112).

^{15} Due to disturbances in demand, reference is made to consumption, investment, State purchases, and economic imports and exports (Jones, 2009: 347-351).

^{16} See Taylor (1998) for the Taylor rule, Hicks (1937) for the is curve and Phillips (1958), Friedman (1968) and Phelps (1968) for the Phillips curve. Also, a more detailed description of what each equation obtains can be found in Pérez (2013).

^{17} The model describes a small and open economy with a free floating exchange rate.

^{18} The demand curve does not contain the product gap, as economic growth is not the monetary policy objective of the country.

^{19} If economic growth is a monetary policy objective, the gap between the product of equation (3) should not be eliminated, resulting in the following aggregate demand curve: (Jones, 2009: 476).

^{20} When the economy is in a long-term equilibrium, the Taylor rule (with one or two targets) is reduced to the expression (Perrotini, 2007: 69).

^{21} Monetary policy must be handled by an *independent *central bank, because this gives greater credibility and commitment to inflation control (Mishkin and Schmit-Hebbel, 2001).

^{22} Inflation targets should be announced to the public in the medium term, as this increases the accountability of the central bank and reduces the change that the banking entity falls into *temporary inconsistencies* (Mishkin, 2000: 2-4).

^{23} When private agents are not fully confident in the commitment of the central bank to meeting its target (imperfect credibility), inflation convergence is slow and the product gap is reduced. When agents are fully confident in the banking institution (perfect credibility), inflation converges quickly to the new target with no reduction in the product gap (Fraga *et al.*, 2004: 7-14).

^{24} By this theory, aggregate supply depends on inflationary expectations (Woodford, 2003), as it is an adjustment factor between inflation and real economic activity.

^{25} If the model were to include economic growth, the aggregate demand curves would be more sloped than in Figure 2, as they would be more sensitive to changes in the product (Jones, 2009: 476).

^{26} Fiscal policy is not viewed as an efficient macroeconomic tool, as monetary policy acts first, requiring fiscal policy to fall in line with it (Mishkin, 2000). As such, if there is irresponsible fiscal policy, there is pressure on authorities to *monetize* the debt, which leads to rapid growth in money and inflation (Mishkin, 2004: 6). Over time, if fiscal imbalances are big enough, monetary policy becomes subordinated to fiscal considerations, which leads to disregard or abandonment of the inflationary target (Mishkin, *op. cit.*).

^{27} The increase (or decrease) of the product is not the only factor that speeds up (or slows down) inflation, because an unemployment rate that is different from the “natural” rate (nairu hypothesis) can also throw the inflation rate off of its target (Perrotini, 2007: 68, 72).

^{28} In practice, it is more useful to interpret inflationary targets as a monetary policy framework, rather than only through the Taylor rule, because when we view them in this way: “central bankers have in practice left themselves considerable scope to respond to current unemployment conditions, exchange rates and other short-run developments" (Bernanke and Mishkin, 1997: 11).

^{29} Together with fiscal stability, a solid and secure financial system is a necessary condition for inflationary targets to be successful, because in a weak banking system, the central bank cannot raise the interest rate to stabilize inflation, without causing a financial collapse due to the outflow of capital (Mishkin, 2004: 6).

^{30} The demand curve from equation (5) was chosen, because it contains the non-linear relationship between inflation and the aggregate economic product (the main objective of this work).

^{31} In econometrics, when there is a set of social units (*i*) whose values are observed over a period of time (*t*), there is cross-sectional longitudinal data (pooled time series) (Pérez, 2006: 675), better known as panel data or panel data regression models for the econometric estimates based on them (Gujarati and Porter, 2010: 591).

^{32} For simplicity, the parameter of equation (8) abbreviates the multiplication of parameters and in equation (5).

^{33} All statistical data used in this work was obtained from the Economic Information Bank (bie) from the National Statistics and Geography Institute (inegi) (see www.inegi.org.mx/sistemas/bie/).

^{34} The igae calculates the monthly production of each of the three economic activities using the same conceptual and methodological scheme employed in calculating the quarterly gross domestic product (gdp).

^{35} Both variables are monthly, but inflation is given in its inter-annual growth rate.

^{36} The types of goods that make up the average inflation in primary activities are: food, drinks and tobacco. For secondary activities: clothing, footwear and accessories, housing, furniture and domestic appliances and accessories. For tertiary activities: health services, personal care, transportation, education, leisure and other services.

^{37} No further elements are included in equation (8), because by estimating the empirical evidence with panel data regressions, there is little information on other economic activities with the same frequency and magnitude. Also, variables like the interest rate, the exchange rate, etc. are read as constants and lead to issues of multicollinearity.

^{38} Table 1 in the next section shows the inflation targets that Mexico has had.

^{39} See www.banxico.org.mx/portal-mercado-cambiario/index.html

^{40} By measuring the inflation targets in Mexico through the ncpi, the distinction of the period of study is made through this index, rather than another.

^{41} Although the period 2000:April/April 2013 does not perfectly coincide with when the inflationary targets monetary scheme took effect, what is important here is not to strictly evaluate its structural effect, but rather its effect on price control (in this case, the change from two to one digit in the ncpi).

^{42} A period prior to 1995 was not chosen, as this would include crisis years that would overestimate the results.

^{43} The representation of the variables (to estimate) by economic activity is shown in Figures 1, 2 and 3 in the statistical appendix. Also, to facilitate understanding, starting with Figure 1, igae and inflation are expressed in annual averages for the period 1995: January/April 2013.

^{44} The ols estimate uses the assumption that variance in error terms is the same for each of the observations (assumption of homocedasticity), and, that these error terms are not correlated for different instances in time nor for different social units (assume no serial correlation) (Baltagi, 2005). This is the same as saying that the error term is like white noise (Pérez, 2006: 680).

^{45} In panel data econometrics, the error term can be broken into (individual component), (temporary component) and (which represents the effect of all other variables that vary between individuals over time) (Pérez, 2006: 680). As such, when there are constant effects and are the same for each of the social agents in the sample over time; when there are fixed effects, only is the same and when there are random effects, both coefficients vary randomly (Pérez *op cit.*, 682-691).

^{46} Stability tests for these two regressions are shown in Tables 1 and 2 in the statistical appendix. Similarly, by following the variables and residuals of these two order of integration models I(1) and I(o), respectively, (see Table 5), there is assumed co-integration of the igae and inflation in both cases (for this reason, the variables have a short and long-term *causal relationship* in their *cross-section longitudinal structures*).

^{47} Regardless of the type of estimators chosen, the tenor of economic analysis is the same, because the effect of inflation on igae falls from the first to the second model (see Tables 1 and 2).

^{48} Another consideration to keep in mind with regards to the above estimates is found in the constant, as it is the same value in both models (this only accentuates the fact that the monetary policy of the country, as an economic measure, does not seek to affect economic growth).

^{49} The inverse relationship between igae and inflation is represented with a negative sign in the trend line equation, and its significance with R2 (see figure 2). Similarly, the above analysis by economic activity is shown in Figures 4, 5 and 6 of the statistical appendix.

^{50} By intrinsic relationship, we refer to a non-linear relationship that corresponds to the very nature of the variables, which may decrease or increase (depending on the economic context), but will never go away.

^{51} By graphing the cycle of igae and inflation by economic activity (see Figures 7, 8 and 9 in the statistical appendix), we also observe the relationship between these two variables over time.

^{52} See Baqueiro *et al.* (2003), Capistran *et al.* (2011), Pérez (2012b) and Cortés (2013) for the transfer of the Exchange rate to prices; Schmidt-Hebbel and Werner (2002), Ball and Reyes (2004) and Nogueira (2007, 2009) for fear of a free floating currency; and Mántey (2009, 2012) for sterilizations in the currency market.