To check if the standardized residuals obtained from the Markow switching GARCH(1,1) model and the Markow switching output growth model are
cor-rectly specified, we apply the standard LM test. For both series we cannot reject the hypothesis of no conditional heteroscedasticity. Thus, we conclude that the Markov switching GARCH(1,1) model for inflation captures the con-ditional heteroscedasticity in both monthly and quarterly US inflation data adequately. Furthermore, the Markov switching model for output growth is properly specified and does not contain any ARCH effects.
Insert Table (6) about here
5 Conclusion
In this paper, we examine the impact of inflation uncertainty on output growth for the US economy. To carry out our investigation, we use two sets of data. The main investigation is carried out on monthly US inflation and industrial production series covering the period 1985:03–2009:08. We then check the robustness of our findings using quarterly GDP series over 1985:QI–2009:QIV. Prior to estimating any model, we investigate the prop-erties of inflation and output growth series. Detecting that both series can be characterized by regime shifts we implement Markov switching models.
In particular, we apply a Markov switching GARCH model to inflation so that we can obtain a measure of uncertainty which considers the shifts in the inflation process. We then construct a Markov switching model for the out-put series to fully capture the growth dynamics as we investigate the impact of uncertainty on growth.
This approach enables us to examine whether the effects of inflation uncer-tainty change across different regimes as the economy expands and contracts.
Similar to the earlier research, we observe a significant and negative effect of inflation uncertainty on output growth. Furthermore, different from the earlier research we show that the negative effect of inflation uncertainty is more pronounced during periods of contraction. In particular, the negative impact of inflation uncertainty on output growth in low growth regimes is about 4.5 times greater than that in a high growth regimes. We also show that the direct effect of inflation on output growth is positive and significant
during low growth regimes while it is negative and insignificant during high growth regimes.
We examine the robustness of our results by re-estimating the model on quarterly GDP series. Once more we detect low and high growth regimes which coincide well with the NBER dates of contraction and expansion for the US economy. The results from this investigation are similar to those findings reported for monthly industrial production data. We observe that inflation uncertainty exerts a negative and larger impact (almost 4 times higher in periods of contraction than that in periods of expansion) on economic growth when the economy contracts. Specification tests provide further evidence that the model is properly specified.
Overall our findings verify that inflation uncertainty exerts a negative impact on output growth through the business cycle. We also observe that uncertainty has stronger negative effects on real economic activity during periods of bottlenecks in economic growth. Our results also show that it is important to use a model that captures the proper behavior of the underlying series to capture the interlinkages between the variables accurately.
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Figure 1: The Inflation Uncertainties in State 1 and State 2
1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 0.00
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
H1 H2
Figure 2: The Inflation Uncertainties Estimated with Single Regime GARCH(1,1) Model and Markov Switching GARCH(1,1) Model
1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 0.00
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08
SRGARCH MSGARCH
Figure 3: Smoothed Probabilities for State 1–1985:03-2009:08
State 1
1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 0.00
0.25 0.50 0.75 1.00
Figure 4: Smoothed Probabilities for State 1–1985:QI-2009:QIV
State 1
1985 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 2009 0.00
0.25 0.50 0.75 1.00
Table 1: Estimation Results for Markov Switching GARCH Model
Parameter Estimate Standard Error
θ01 0.002*** 0.000
θ11 0.218*** 0.089
θ02 0.002*** 0.000
θ12 0.420*** 0.065
α01 0.000*** 0.000
α11 0.185* 0.103
α21 0.033 0.125
α02 0.000 0.000
α12 0.162*** 0.057
α22 0.724*** 0.155
P11 0.991‡ 0.009
P22 0.995‡ 0.004
Log-likelihood 1343.151
Notes: *, **, *** denote significance at the 10%, 5% and 1% levels.
‡ significance of P11 and P22 is relative to 0.5.
Table 2: Estimation Results of Equation (6)–1985:03-2009:08 Parameter Estimate Standard Error
φ01 0.001*** 0.000
β11 0.021 0.070
β21 0.328*** 0.053
β31 0.257*** 0.059
φ02 0.000 0.002
β12 0.277** 0.130
β22 0.051 0.153
β32 0.053 0.157
σ01 0.004*** 0.000
σ02 0.011*** 0.001
P11 0.947*** 0.023
P22 0.808** 0.093
Log-likelihood 1324.364
Notes: *, **, *** denote significance at the 10%, 5% and 1% levels.
Table 3: Estimation Results of Equation (5)–1985:03-2009:08 Parameter Estimate Standard Error
φ01 0.002*** 0.001
β11 -0.001 0.066
β21 0.294*** 0.057
β31 0.202*** 0.054
ϕ11 -0.135 0.110
δ01 -0.087* 0.053
φ02 0.003 0.002
β12 -0.121 0.182
β22 -0.242 0.220
β32 -0.282 0.265
ϕ12 0.699* 0.424
δ02 -0.383*** 0.129
σ01 0.004*** 0.000
σ02 0.010*** 0.002
P11 0.948*** 0.025
P22 0.664*** 0.118
Log-likelihood 1117.299
Notes: *, **, *** denote significance at the 10%, 5% and 1% levels.
Table 4: NBER Dates of Expansions and Contractions Business Cycles Reference Dates Duration in Months
Peak Trough Contraction Expansion
July 1990(III) March 1991(I) 8 92
March 2001(I) November 2001 (IV) 8 120
December 2007 (IV) June 2009 (II) 18 73
Source: National Bureau of Economic Research (NBER), Quarterly dates are in parentheses.
Table 5: Estimation Results of Equation (5)–1985:QI-2009:QIV Parameter Estimate Standard Error
φ01 0.009*** 0.001
β11 -0.070 0.110
β21 0.248*** 0.097
β31 -0.068 0.119
ϕ11 0.031 0.093
δ01 -0.152* 0.089
φ02 0.008*** 0.002
β12 0.420*** 0.095
β22 0.127 0.093
β32 -0.648*** 0.083
ϕ12 -0.023 0.055
δ02 -0.603*** 0.092
σ01 0.004*** 0.000
σ02 0.002*** 0.001
P11 0.875* 0.066
P22 0.592*** 0.165
Log-likelihood 390.711
Notes: *, **, *** denote significance at the 10%, 5% and 1% levels.
Table 6: ARCH LM Test for Squared Standardized Residuals Output Growth Inflation
Equation Equation
1985:01-2009:08 ARCH LM test 0.021 7.136
(monthly data) (lag=4) [0.999] [0.129]
1985:QI-2009:QIV ARCH LM test 0.422 (quarterly data) (lag=4) [0.981]
Notes: p values in square brackets.