Determination of inflationary behavior: A comparative analysis

Abstract Standard theory of consumer behavior stands on the maxim of utility maximization. Optimizing behavior of consumer is achieved by maximization of utility subject to budget constraint. An increase in inflation that is not accompanied by proportionate increase in income can leave a consumer worse off. Therefore, it is imperative for consumers to have right assessment about inflation which in turn requires appropriate modelling of inflationary behavior. This study assesses efficacies of different versions of new Keynesian Phillips curve for capturing dynamics of CPI inflation. Estimation of different formulations of this curve is achieved by employing generalized method of moments. This choice of estimation technique is made to handle potential problem of endogeneity. Countries with different resource and market structures are included to evaluate and compare fitness of different formulations for different economies. Economies of Pakistan and Turkey represent developing economies, economy of South-Korea is incorporated for emerging market economy and economies of Canada, UK and US are included for developed economies. The results of this study reveal that internal as well as external factors are crucial for explaining inflationary behavior of developing economies. Whereas, dynamics of domestic inflation for advanced economies are mostly explained by internal factors.


PUBLIC INTEREST STATEMENT
This study tries to explore the sources that cause changes in prices and tries to capture the dynamics of price changes. Potential sources of such changes in prices can be traced from domestic factors while external factors could also be important for determining price changes at the domestic level. This study is helpful for understanding dynamics of inflation. Unstable fluctuations in prices are problematic for consumers and producers as their decisions regarding consumption and production are disturbed by such changes. Therefore, if policy maker can figure out main sources of changes in inflation and keeping those sources stable can lead to stable behavior of inflation. This study is essential for understanding main sources of inflation.

Introduction
Prices are signals for consumers that direct their consumption decisions. Once there is inflation and it is not aligned with equal increase in income, then this would mean a reduction in real incomes of consumers. Such an incident would leave a consumer at lower indifference curve which means that he is obtaining less utility without reduction in work. Hence, it is imperative for consumers to know exactly the factors that affect changes in inflation otherwise they will be exploited.
Economic models of price dynamics are built to explain contributory factors that can influence prices. For instance, an economic model that is built on quantity theory of money would relate one-to-one changes in inflation with growth of money supply. Such a model is very intuitive but lacks supply side linkages. A more comprehensive models would relate price changes with supply side changes along with external factors.
New Keynesian Phillips curve (NKPC) has an advantage that it relates changes in current inflation with output changes from potential level. NKPC also accounts for any potential inertia that represents feedback effect that builds from demand side pressures. Other versions of NKPC also incorporate external factors that contribute to domestic inflation such as exchange rate changes and world inflation.
The purpose of this study is to estimate, analyze and compare different versions of NKPC for countries with diverse resource and market structures. Inclusion of countries that belong to different developmental stages allows us to compare efficacies of different formulations of this curve for capturing inflationary behavior in different resource and market structures. To achieve this end, developing economies of Pakistan and Turkey, emerging market economy of South-Korea and developed economies of Canada, U.K. and U.S. are made part of this study.
There are different measures of inflation such as consumer price index (CPI), gross domestic product (GDP) deflator, whole sale price index and producer price index. This study tries to evaluate extent to which NKPC successfully encompasses dynamics of CPI inflation. CPI inflation represents headline inflation and this is a measure of inflation that matters the most for consumers. Therefore, successful assessment of CPI inflation is necessary for a consumer to make optimal consumption decision.
Second section of this study yields findings of some past studies that are pertinent to countries involved. Third section is about explanation of variables and sources of data sets that are used for empirical evaluation of different versions of NKPC. Methodological framework is also explained in third section. Second last section of this study provides results from estimated versions of NKPC along with analysis. Last section is devoted for conclusions and policy implications that are derived from results and analysis section of this study.

NKPC: past experiences
The NKPC curve started with development of micro-foundations of macroeconomic models by Fischer (1977), Taylor (1980), Rotemberg (1983), and Calvo (1983) resulted in real effects of monetary side even in the presence of rational expectations. Mankiw (2001) formulated the NKPC, based on monopolistic competition and sticky prices, establishes a relationship between inflation and economic activity. Mankiw (2001), however, found his formulation at odds with facts.
Sbordonne (2001) pointed that NKPC yields reasonable predictions only when output gaps truly represents marginal costs. Gali and Gertler (1999) developed a hybrid NKPC that includes lag and lead of inflation. According to hybrid NKPC, it was assumed that both past and future inflations came into consideration for setting current prices. Gali et al. (2001), (2003) and (2005) estimated NKPC and new hybrid new Keynesian Phillips curve (NHKPC) for Euro area and found superior fit of NHKPC, whereas lagged inflation effect appeared in explaining current inflation in euro area in comparison with U.S. economy. Leith and Malley (2007) evaluated the performance hybrid NKPC for Canadian economy and found lesser price inertia for this economy which was similar to the findings for U.K. and U.S. economies. Kozicki and Tinsley (2002) estimated different specification of NKPC for Canadian economy and found hybrid version as a better fit for this economy. Gagnon and Khan (2005) estimated different specifications of NKPC and found strong effect of lagged inflation for explaining current inflation for Canadian economy in comparison with US and Euro area. Barkbu and Batini (2005) found NKPC as a better fit for inflation of Canada for some measures of marginal cost. On the other hand, Guay et al. (2003) rejected the NKPC for Canadian economy once bias in GMM estimation is corrected. Moon et al. (2004) found hybrid new Keynesian Phillips curve for Korean economy captures the dynamics of inflation for this economy. Yoo and Ahn (2006) and Kim and Ahn (2008) also reached the same conclusion for Korean economy. Onder (2004) showed better forecasting of Turkish economy through output gap. Yazgan and Yilmazkuday (2005) and Catik, Martin et al., (2008) refuted presence of hybrid NKPC for Turkish economy. Agénor and Bayraktar (2010) found output gap as insignificant predictor of Turkish inflation, whereas lagged inflation appeared to be more significant than expected inflation for this economy. Saz (2011) estimated conventional and hybrid NKPC for Turkish economy and found these specifications as valid for this economy. Satti et al. (2007) found more support for forward-looking inflationary behavior for economy of Pakistan. However, Saeed and Riaz (2011) found hybrid version of the Phillips curve to be more explanatory for inflationary behavior in Pakistan. Mukhtar and Yousaf (2014) also found supporting evidence for hybrid version of NKPC and found backward looking instead of forward looking behavior as more dominant factor for explaining inflation for Pakistan. Riffat et al. (2016) found terms of trade and trade openness play a significant role for explaining inflationary dynamics in Pakistan.

Data sources and methodological framework
This section introduces variables that are used in this study and sources of these data sets. Moreover, methodological framework is also provided in this section.

Data sources
Estimation of NKPC involves variables such as CPI inflation, real GDP, agricultural output, manufacturing output, industrial production, industrial production index, exchange rate, discount rate, federal funds rate, GDP deflator, whole sale price index, primary inflation, eggs' inflation and monetary aggregate M2 for all other economies and M4 for UK.
Sources of these data sets for economy of Pakistan are handbook of statistics published by the state bank of Pakistan (SBP) and Pakistan economic survey published by ministry of finance under federal government of Pakistan. Sources of data for economies of Turkey, South-Korea, Canada, UK and US are OECD, 1 IMF, 2 World Bank, Federal Bank of St. Louis and source of eggs' inflation is FAO 3 statistics. Time span of data is from 1973 to 2016 for all economies and frequency of data is annual.

NKPC: methodological framework
Different equations along with instruments are shown in Table 1 of Appendix A.1. Equation (1) is the traditional backward looking Phillips curve. Equation (1) shows that current CPI inflation (π t ) is determined by previous year inflation and previous year output gap (ŷ t ). Equation (2) augments the world inflation (π w t ) along with exchange rate changes (dlex t ). Hence, it provides an open economy version of traditional Phillips curve. Third equation (3) is a forward-looking NKPC that includes lead of inflation to measure the role of expected inflation in determination of current inflation. Equation (4) is an open economy version of forward-looking NKPC. Equation (5) is the hybrid specification of NKPC, i.e. it incorporates lead and lag of inflation. Last equation (Equation 6) is open economy version of hybrid NKPC.
Above mentioned equations are estimated by generalized method of moments (GMM) with specified instruments. Appeal for this approach is due to possibility of endogeneity in NKPC. Possibility of endogeneity problem is due to potential correlation between expected future inflation and error term in the equation of NKPC. Error term in the equation of NKPC represents forecast error of inflation. Therefore, this forecast error of inflation can be correlated with the expected inflation. Moreover, this technique is robust to serial-correlation and heteroscedasticity of unknown form. Hence, it is superior to two stage least squares (TSLS). Table 2 of Appendix A.2 shows results from the specifications of NKPC that are estimated in this study. Results are shown only for those models that provided the best fits for respective economies. Best models are selected on basis of maximum adjusted R-squared and minimum standard error of regression after removal of insignificant variable. Regression results for all economies show that lag of output gap has statistically significant effect on inflation of all economies at 5 percent level of significance except for economy of South-Korea. A one percentage point increase in lag of output gap leads to 0.14 percentage points increase in current inflation for economy of Pakistan, 0.35 percentage points increase for economy of Turkey, 0.06 percentage points increase for Canada, 0.21 percentage points increase for UK and 0.15 percentage points increase for US.

NKPC: results and analysis
Lag of inflation is also statistically significant for all economies at 5 percent level of significance. A one percentage point increse in lag inflation increases current inflation by 0.27 percentage points for economy of Pakistan, 0.54 percentage points increase for economy of Turkey, 0.33 percentage points increase for economy of South-Korea, 0.43 percentage points increase for economy of Canada, 0.62 percentage points increase for economy of UK and 0.35 percentage points increase for economy of US.
Expected inflation is statistically significant for economies of Turkey, South-Korea, Canada and US. showing 0.21,0.27,0.37 and 0.46 percentage points increase in current inflation in response to one percentage point increase in expected inflation. The role of world inflation is also statistically significant for all economies. A one percentage point increase in world inflation increases current inflation by 0.89 percentage points for Pakistan, 0.78 percentage points for Turkey, 0.50 percentage points for South-Korea, 0.18 percentage points for Canada, 0.38 percentage points for UK and 0.18 percentage points for US. However, influence of exchange rate is statistically significant only for develeoping economies of Pakistan and Turkey.
Therefore, it seems that past inflation is important for building momentum of current inflation for all economies, whereas expected inflation also playes important role for current inflation except for economies of Pakistan and UK. External factor such as world inflation also affects domestic inflation significantly for all economies. Whereas, fluctuations in exchange rate matters for inflation of developing economies of Pakistan and Turkey. The values of J-statistics and respective probabilities show that all over-identifying instruments are valid.

Conclusions and policy implications
This study is conducted to measure influences of internal as well as external factors on domestic inflation. Different specifications of NKPC are estimated to evaluate performance of each specification for capturing dynamics of inflation. Role of past inflation is important for determing current inflation. Whereas expected inflation has also significan influence on CPI inflation, but not for economies of Pakistan and UK. It seems that inflation in developing economies is prone to external factors in comparison with relatively advanced economies of this study.
It is very clear that CPI inflation in developing economies is affected by external factors, whereas dynamics of domestic inflation for developed economies are largely captured by internal factors. Therefore, forecasts of CPI inflation for developing economies should be based on open economy version of NKPC so that information regarding expected inflation can be calculated correctly. Furthermore, information regarding these expected estimates can be shared with consumers so that they can maintain their existing level of utility by demanding an equiproportionate changes in their incomes.