Author's Notes: Tonight's post will be a continuation of July 2nd's post, where I utilized economic data to generate econometric models to measure domestic consumption. This post was a follow-up course deliverable to the previous post's course deliverable, where I utilized regular and logged OLS regression on macroeconomic data to model domestic consumption. Tonight's post will not only utilize regular regression once again, but will also introduce a dynamic regression model, which will be created by lagging key explanatory variables to account for time-based trends in the data.
In addition, I created a public Twitter account, where I will not only share and discuss current events, news articles, and anything that comes up in my life, but will also post updates and announcements regarding this blog.
Methodology: The same variables and theorized relationships are ported over from the earlier post's data (linked above), although Disposable income as savings (%) and Real public consumption and investment were dropped from the models in this post after determining that they were not suitable. Year was also dropped to avoid interfering with the lagged variables that will be created later. For each regression model, robust standard errors were utilized to account for possible heteroscedasticity.
Model 1 will utilize regular OLS as a baseline to compare the dynamic models to. Model 2a will use OLS regression, but will lag the response variable (consumption) one time period and include it as an explanatory variable, while Model 2b will lag consumption by two times periods, and include the lagged version as an explanatory variable. Model 3 will include both lagged versions of consumption as explanatory variables. Prior to calculating regression, I will first perform the Durbin-Watson test on Model 2a to determine whether the errors within the model are serially-independent. The four models are constructed as follows:
- Model 1: Yi Consumption = β0 + βn [All Explanatory Variables] Xn + ε
- Model 2a: Yi Consumption = β0 + βn [All Normal Explanatory Variables] Xn + (lagged 1x) βn Consumption Xn + ε
- Model 2b: Yi Consumption = β0 + βn [All Normal Explanatory Variables] Xn + (lagged 2x) βn Consumption Xn + ε
- Model 3: Yi Consumption = β0 + βn [All Normal Explanatory Variables] Xn + (lagged 1x) βn Consumption Xn + (lagged 2x) βn Consumption Xn + ε
Results:
Table 1: Regression Results
*p < .05, ** p < 0.01, *** p < 0.001
Notes: Values in parentheses indicate robust standard errors, which account for possible heteroscedasticity in the data.
The Durbin-Watson result for Model 2a is .9775, meaning that the errors are positively auto correlated (Kenton). Based on this result, the errors in the model are not serially independent due to the positive autocorrelation.
Table 1 displays the regression results. In the base OLS model, Model 1, after deleting the variables described above, average prime rate (%), total disposable income, and civilian unemployment rate (%) are statistically-significant at the 5% level or lower. After inserting consumption lagged one time as an explanatory variable in Model 2a, the only change is that time deposits becomes statistically-significant at the 5% level, while the new lagged variable is statistically significant at the 1% level. In Model 2b, replacing consumption lagged once with consumption lagged twice results in Time deposits no longer being statistically significant at the 5% level, and the new lagged consumption variable not being statistically significant at the 5% level. Finally, by using both lagged consumption variables as explanatory variables in Model 3, only consumption lagged once is statistically significant at the 5% level or lower, while civilian unemployment rate (%) is no longer statistically significant at the 5% level or higher.
Analysis and Implications: Based on the results detailed above, the twice-lagged consumption explanatory variable does not seem to be a good fit, and it can even be argued to be detrimental to the rest of the model, while the once-lagged consumption explanatory variable is a better (not perfect) fit. Through inference, there are two possible reasons the once-lagged version is a better fit than the twice-lagged version. The first effect may have to do with the history of price changes that influence the total real value of domestic consumption. Throughout the time period studied by this assignment (1950 to 2018), a major point when marginal real price changes began to increase was around 1969, when the marginal rate of inflation reached 5%, and generally remained at that level for the next 15 years, a substantial time period in this assignment’s timeline, with high rates of inflation being seen in certain years ("Consumer Price Index, 1913--"). Around 1984, this trend began to decline slowly to the pre-1969 inflation rate ("Consumer Price Index, 1913--"). Depending on where the Stata calculations “placed” the lag on the timeline, it could be that this notable time period was split between the two “sections” separated by the lag on the single lagged model, making both sections relatively homogeneous in terms of the variation in consumption relative to price changes. On the double-lagged model, this section may have received its own “section,” which could have skewed the results. My second theory is that constricting down the number of variables from the previous assignment, particularly disposable income as savings (%), may have skewed the remaining variables because disposable income as savings (%) was statistically-significant in all three models presented in Assignment 1.
Based on the results in this assignment, for aggregate time series data, I think that dynamic models are generally more likely to provide a better model fit than regular models under certain circumstances. Particularly, I think this holds true if one is using a time series data with a relatively large variation in the dependent variable values and the timeframe being studied (both of which are true here). This is because the purpose of the lag is to account for changes over time that build on existing data, such as future stock prices, which essentially depend on previous stock prices ("Chapter 8"). This is because some changes on the dependent variable may not happen immediately, which lagged explanatory variables are meant to account for this change ("Chapter 8"). As such, it could be argued that the use of lagged explanatory variables is best used when extrapolating current results to provide future predictions, as one has take into account the micro-changes within the dependent variable that can influence the speed at which that variable changes.
Works Cited:
"Chapter 8: Regression with Lagged Explanatory Variables." personal.strath.ac.uk/gary.koop/Oheads_Chapter8.pdf. Accessed 11 Nov. 2019.
"Consumer Price Index, 1913--." CPI Calculator Information, Federal Reserve Bank of Minneapolis, www.minneapolisfed.org/community/financial-and-economic-education/cpi-calculator-information/consumer-price-index-and-inflation-rates-1913. Accessed 11 Nov. 2019.
Kenton, Will. "Durbin Watson Statistic Definition." Investopedia, 18 Jul. 2019, www.investopedia.com/terms/d/durbin-watson-statistic.asp. Accessed 11 Nov. 2019.
Data Source:
Bhargava, Alok. In the author's possession.
Nathan Parmeter
Host and Author, The Parmeter Politics and Policy Record
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