Journal Issue


International Monetary Fund
Published Date:
August 2011
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I. Potential Growth and the Output Gap in Mexico1

Decomposing the growth process in trend and cyclical factors represents an important challenge, with implications for policy decisions. This paper applies several methodologies to the case of Mexico and tries to assess to what extent these methodologies adequately capture cyclical changes. The results suggest that care is needed when using these indicators in real time to assess the stage of the cycle, particularly in the presence of large shocks, and that a variety of macroeconomic indicators are needed to evaluate and validate the results.

A. The Output Gap

1. Estimates of the output gap are important for the conduction of macroeconomic policies. The central bank’s inflation targeting framework entails assessing if the projected output implied by the monetary policy stance is consistent with the inflation target. A measure of the output gap is also helpful to assess the stance of fiscal policy and fiscal sustainability—even when the fiscal rule is not a structural one.

2. However, estimating the output gap entails significant challenges. Since potential output is not directly observable, it has to be inferred from the data. However, changes in actual output could reflect cyclical shocks or permanent impacts to potential output. Inferring whether a shock is cyclical or temporary can be a difficult task. As a result, an ample array of methodologies has been used in the literature to estimate the output gap, with filters frequently used to separate cyclical and structural components. It should be noted, however, that these estimates are subject to substantial uncertainty.

3. The end-point problem is particularly important. Some of the methodologies employed, including the HP filter, have been criticized on several grounds, including that the end-point has too much of an impact on the trend of the series. While this could be addressed, it is still hard to correctly identify a shock in real-time, with subsequent data providing relevant information, which can result in estimates that are not consistent across time. Several approaches have been used to reduce the weight of the last observation—including through the use of forecast—while multivariate filters use different variables in an attempt to identify the nature of the shock.

4. The pre-crisis period entails an interesting test to these methodologies. The unusually large cycle associated with the global crisis makes identifying cyclical and structural components a challenge. The availability of some post-crisis data allows us to compare real time and full sample results to assess their consistency.

5. We estimate the output gap applying different methods. Using real GDP quarterly data from 1990 to 2010, we followed two different approaches: (i) a Kalman filter of unobserved components approach (with univariate and multivariate models) and (ii) a production function approach. The Kalman filter approach includes models used by Fuentes et al (2007), Marcet and Raven (2004), and Clark (1987), while the production function approach follows Krajnyak (2010).

Univariate filters

6. A univariate HP filter is probably the most popular approach. This method entails minimizing the square deviations from the trend (which basically penalizes the cyclical component) and the squared changes in the trend component (which penalizes variations in the growth rate of the structural component). When they proposed this method Hodrick and Prescott (1997) set the smoothness of the trend (lambda=1600) such that the resulting cyclical patterns made sense using US post-war data. This smoothness parameter has become the standard when estimating the output gap, even though studies like Marcet and Ravn (2004) contest its validity outside the US.

Output Gap as a Share of Potential Real GDP

(HP Filter, Lambda = 1,600)

Sources: INEGI, and Staff Calculations

7. This approach suggests a large pre-crisis positive output gap, using full sample data. The real-time estimates, however, suggest the gap was nil in 2008. The large decline in output following the 2008 financial crisis is behind the difference between the two estimations. The estimated pre-crisis potential output in the full sample is lower than the one using just pre-crisis data, as the filter assigns some of the decline to the structural component. Therefore, and given that changes in the growth rate of potential are penalized, the decline in the estimated potential “anticipates” the crisis.

8. Changing the smoothness of potential growth yielded similar results. A higher penalty on changes in potential growth entails a smaller decline in the estimated potential following the crisis. The higher potential output entails smaller positive output gaps. Calculations using two arbitrary lambdas (5,600 and 10,000), and Marcet and Ravn “W” model entail smoother potential growth and yield lower (but still positive) output gaps; while Marcet and Ravn “V” model implies a less smooth potential and a somewhat higher gap. Real-time estimates remain inaccurate, particularly right before the global crisis.

5. We estimate the output gap applying different methods. Using real GDP quarterly data from 1990 to 2010, we followed two different approaches: (i) a Kalman filter of unobserved components approach (with univariate and multivariate models) and (ii) a production function approach. The Kalman filter approach includes models used by Fuentes et al (2007), Marcet and Raven (2004), and Clark (1987), while the production function approach follows Krajnyak (2010).

Univariate Filter: Alternative Smoothness Parameters

Sources: INEGI, and staff calculations.

9. Increasing the persistence of the cyclical component improved the performance. An alternative to the HP filter is an unobservable component model a la Clark (1987). This assumes that the cyclical component follows a second-order autoregressive process.2 The consistency between real time and full sample estimates improves for the pre-crisis period. This should not be surprising, as the model builds on persistence in the cyclical component.3

Output Gap as a Share of Potential Real GDP

(AR(2) Model, Lambda = 1,600)

Sources: INEGI, and staff calculations.

Multivariate filters

10. Information from macroeconomic relations could help improve univariate filters. We estimated the output gap using the Phillips Curve, the IS Curve,4 and Okun’s Law, as in Fuentes et al (2007). Core inflation, as defined by the Mexican authorities, is used in all three models. A backward looking Phillips curve is used as second signal equation in the first multivariate filter; the second one incorporates a standard backward looking IS curve; finally, while the third model builds on the first one by adding Okun’s Law.

11. Using a Phillips Curve and an IS curve in the multivariate filter did not yield significantly different results to the univariate filter. Similar to the univariate HP filter, the real-time results suggest a 3 percent positive gap right before the crisis, while the full-sample results yielded larger gaps.5 The lack of significant improvement from adding a Philips curve is not surprising, considering that Ramos-Francia and Torres (2006) found a small and non-significant coefficient for a backward-looking Phillips curve.

Multivariate filters: Phillips Curve and IS Curve

Sources: INEGI, Banxico, and staff calculations.

12. The multivariate filter using Okun’s Law shows less cyclical movements. Given that the actual rate of unemployment increased following the crisis, and has remained above pre-crisis levels, we added an equation relating unemployment to the output gap. While the results were sensitive to the choice of potential output’s smoothness, all of them showed a pre-crisis negative output gap using real-time estimates. Also, the time consistency of this model is superior to the univariate and the bivariate filters using the Phillips and IS curves, albeit not so for the pre-crisis period.

Multivariate Filter: Okun’s Law Using Different Smoothness Parameters.

Sources: INEGI, Banxico, and staff calculations.

Comparing models

13. The substantial variation in results, particularly when considering real-time estimates, suggests caution should be used. Most models yielded different results for the pre-crisis gaps using real-time and full sample estimates. We performed two tests based on Fuentes et al (2007) to assess which models perform better in terms of both internal consistency (i.e., comparing real time vs. full sample estimates) and inflation forecasting.6

14. Time consistency of the estimates. We compared the results from real-time and ex-post estimation for the battery of models. We carried out the exercise for the period 2000—2009.7 Some of the models had quite strong consistency, as suggested by high correlations and relative small squared errors—with persistence in potential growth helping as expected.

Table 1.Internal Consistency Check: Comparison Between Real-Time and Ex-Post Estimation
MethodsCorrelation between real-time and ex-post estimationSquared root of the MSESquared root of the MSE for period 2007Q2-2008Q2
Univariate model, lambda = 1,6000.640.30%0.63%
Univariate model, lambda = 5,6000.780.25%0.62%
Univariate model, lambda = 10,0000.830.21%0.64%
Bivariate model, Phillips Curve, lambda = 1,6000.620.30%0.62%
Bivariate model, Phillips Curve, lambda = 5,6000.760.25%0.62%
Bivariate model, Phillips Curve, lambda = 10,0000.820.22%0.64%
Bivariate Model, IS Curve, lambda = 1,6000.530.24%0.68%
Bivariate Model, IS Curve, lambda = 5,6000.680.24%0.68%
Bivariate Model, IS Curve, lambda = 10,0000.760.20%0.61%
Bivariate Model, Okun’s Law, lambda = 1,6000.600.16%0.68%
Bivariate Model, Okun’s Law, lambda = 5,6000.660.16%0.68%
Bivariate Model, Okun’s Law, lambda = 10,0000.800.20%0.83%
Clark restricted model (Univariate AR(2)), lambda =1,6000.830.12%0.12%
Clark restricted model (Univariate AR(2)), lambda =5,6000.900.13%0.56%
Clark restricted model (Univariate AR(2)), lambda =10,0000.900.12%0.48%
“V model”0.560.30%0.65%
“W model”0.720.28%0.62%

15. Forecast performance of the estimates. We compared the root mean squared error of two alternative forecasting models: a benchmark inflation autoregressive model and an extended model that added the real-time output gap estimates.

Table 2.Relative RMSE: Real-Time Output Gap Estimates/Inflation AR Models
Method1 Q Ahead2 Qs Ahead4 Qs Ahead6 Qs Ahead
Univariate model, lambda = 1,6001.000.970.840.86
Univariate model, lambda = 5,6000.980.930.810.83
Univariate model, lambda = 10,0000.970.920.800.82
Bivariate model, Phillips Curve, lambda = 1,6001.000.970.840.87
Bivariate model, Phillips Curve, lambda = 5,6000.980.930.810.83
Bivariate model, Phillips Curve, lambda = 10,0000.970.920.800.82
Bivariate Model, IS Curve, lambda = 1,6001.010.980.850.87
Bivariate Model, IS Curve, lambda = 5,6000.980.930.810.83
Bivariate Model, IS Curve, lambda = 10,0000.980.920.800.82
Bivariate Model, Okun’s Law, lambda = 1,6001.010.940.810.83
Bivariate Model, Okun’s Law, lambda = 5,6000.980.910.790.81
Bivariate Model, Okun’s Law, lambda = 10,0001.000.920.800.82
Clark restricted model (Univariate AR(2)), lambda = 1,6000.960.890.770.79
Clark restricted model (Univariate AR(2)), lambda = 5,6000.960.890.780.80
Clark restricted model (Univariate AR(2)), lambda = 10,0000.960.890.770.80
“V model”1.010.940.810.84
“W model”0.990.920.800.82

B. Trend Growth

16. During the last three decades, growth has averaged 2.5—2.75 percent. Even during the pre-crisis period, growth was below 3.5 percent on average. Recent papers have tried to explain these results pointing to a large list of factors.8

Table 3.Growth in Mexico, 1980–2010
MaximumMinimumMeanMedianShare of observations

above 3.25%
I. Rolling averages2000Q45.51987Q1-
5-Year moving average1994Q43.71989Q20.52.62.722.0
7.5-Year moving average2000Q33.71991Q41.52.72.730.0
10-Year moving average
II. Selected periods

17. Potential growth was estimated using growth accounting. Growth is decomposed in the contribution from capital and labor inputs, with TFP calculated as a residual. The distribution in cyclical and structural factors is made at the disaggregated level using a simple HP filter—subject to all the caveats mentioned earlier—albeit incorporating staff forecasts for these variables to limit end-point problems. The purpose is to assess how much can be explained by labor and capital accumulation, as opposed to TFP, which is harder to estimate, and for which an underlying historical growth rate is used. Similar to Krajnyak (2010) we build series for the capital stock and labor input. A share of 33 percent for capital and 67 percent for labor is used.9

  • Capital stock was estimated applying the perpetual inventory methodology to the gross fixed capital formation (excluding residential investment) series presented by INEGI, assuming an annual depreciation of 7.5 percent.10

  • Trend capacity utilization was assumed to stabilize around 80 percent from 2011, which is the historical average for this series.

  • The historical data for working-age population and participation rate was taken from the World Bank’s World Development Indicators, while the estimates for 2011-16 are based on CONAPO’s projections.

  • The structural unemployment rate is assumed to stabilize at 3.5 percent starting in 2013. This figure is also in line with the results obtained in the Okun’s Law filter exercise.

18. Potential growth is estimated at 3-3¼ percent, driven by labor and capital accumulation. Our calculations show rather unchanged contributions of labor and capital to potential growth, as well as marginal improvements in TFP. Stable labor and capital contribution and low TFP growth is consistent with potential growth around 3-3¼ percent, in line with Mexico’s previous economic performance, and OECD (2009) and Krajnyak (2010) estimates. This also suggests that enhancing TFP is required to achieve higher long term growth, with recent reforms moving in that direction.

Figure 1.Mexico: Growth Accounting, 1991–2016

INEGI, Banxico, WEO, Haver Analytics, CONAP, and staff estimates.

Figure 2.Mexico: Output Gap and Other Macroeconomic Indicators, 2000-2010 1/

Source: Banxico, Haver Analytics, INEGI, and IMF staff calculations

1/ Calculated using HP filter, lambda = 1,600

2/ Defined as the difference between CETES to 28 days and Y/Y changes


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    FaalEbrima.“GDP Growth, Potential Output, and Output Gaps in Mexico.”IMF Working Paper No. 05/932005: 30.

    FuentesRodrigoFabianredig and MauricioLarrain.“Estimating the Output Gap for Chile.”Central Bank of Chile Working Paper No. 455December2007: 29.

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Prepared by Enrique Flores and Francisco Vazquez-Ahued.

This is different from the HP filter approach, which implicitly assumes a model with cyclical and structural shocks that follow a random walk.

Different values of lambda were tried, always obtaining a negative output gap.

Mexico officially adopted an inflation targeting regime in 2000. In order to estimate the inflation objective prior to that year, we used the inflation target estimates presented by Galindo and Ross (2005) from 1995 to 1999. For the period between 1990 and 1994, we assumed that the target was equal to 80 percent of the realized y/y inflation. We also assumed that the policy interest rate was equal to the 28 days CETES rate before the introduction of a policy rate by Banxico.

The graphs shown in panel 2 correspond to a lambda equal to 1,600. We also estimated the models setting lambda equal to 5,600 and 10,000, with results similar to those using the univariate filter.

A robustness test was performed for starting in 1997 in order to have two full economic cycles. The results did not change significantly.

The sample was limited to 2009 in order to avoid the end-point problem mentioned above.

Our results would not change significantly if we assume a 60 percent share of labor, as found by Garcia-Verdu (2005).

The results presented by Garcia-Verdu (2005) use a depreciation rate of 5 percent. As a robustness test, we used such depreciation rate and the results for TFP growth did not change significantly.

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