MODELS FREQUENTLY ENCOUNTERED IN THE STUDY OF ECONOMETRICS Econometrics is the application of statistical method to economic ...

- MODELS FREQUENTLY ENCOUNTERED IN THE STUDY OF ECONOMETRICS

**Econometrics is the application of statistical method to economic data and is described as the branch of economics that aims to give empirical content to economic relations (Pesaran, 1987). The first known use of the term "econometrics" (in cognitive form) was by Polish economist Pawel Crompa in 1910 (wikipedia). Ragner Frisch is credited with coining the term in the sense which it is use today (Pesaran, 1990).**

**According to Gujarati and Porter (2009), econometrics is the amalgam of economic theory ,mathematical economics, economic statistics ,mathematical statistics . In other words, econometrics is the application of mathematical economics and statistics for structural analysis in economics that will allow for policy evaluation and forecasting/prediction.**

**Felix Chan PhD econometrics, university of western Australia wrote "Econometrics modeling goes beyond prediction". At its core, econometric concern mostly with verifying economic hypothesis empirically. While econometrics, especially time series econometrics, offers techniques for forecasting and/or prediction purposes, its applications in economics and finance are not limited to prediction. Moreover, econometrics is not generally satisfied with a good prediction, it also need to understand why the prediction works from the perspective of econometric theory .It is the connection between statistics, mathematical modeling and economic theory that makes econometric unique.**

**Econometric model specifies the statistical relationship that is believed to hold between the various economic quantities pertaining to a particular economic phenomenon under study .An econometric model can be derived from a deterministic economic model by allowing for uncertainty or from an economic model which itself is stochastic. However, it is also possible to use econometric models that are not tied to any specific economic theory (Sims,1980).**

**TYPES OF MODEL**

**These are various types of models frequently encountered in the study of econometrics modeling. The major types of model are static and dynamic.**

**Static model, time does not play any role. In essence, the models in this category, the role of time is not essential. To illustrate, consider the following consumption, income and wealth relationship.**

**C**

_{t }= Ω_{0 }+ Ω_{1}Y_{t }+ Ω_{2}W_{t }+ U_{t (1)}

**The above equation is static in the sense that variations in the left hand side variable (endogenous) at a point in time are on account of variations in the right hand side variables (exogenous) at that time. In the case of dynamic models, the role of time is essential. The recognition of the role of time is accomplished through the inclusion of lead, and/or lag variables in the specification. Model including such variables are closer to real life, it is usually more realistic to introduce dynamism into our model specification. In doing this, consider the general autoregressive distributed lag (ARDL) model below.**

C

C

_{t}= £_{1}C_{t-1 }+ Ω_{0 }Y_{t }+ Ω_{1}Y_{t-1 }+ U_{t (2) }

**The equation above shows a variant of dynamic specification .Equation 2 is a dynamic model because it include not only Y**

_{t}and Y_{t-1}as explanatory, but also , a lagged dependent variable (C_{t-1}) as an explanatory variable. Our interest is to take a close look at the various forms of dynamic models that are in commonplace in econometric analysis.

1. Univariate Autoregressive models (UAM)

1. Univariate Autoregressive models (UAM)

**To derive the UAM model, we take example of a first order Autoregressive model or AR(1) by setting Ω**

_{0}=Ω_{1}=0

C

C

_{t}= £_{1}C_{t-1 }+ U_{t (3) }

**The elegance of the univariate autoregressive model is that with it, it is possible to overcome the problem of static regression. However, the UAM is not without its own limitations, the major one being that the lag introduced into the specification is not an autonomous process, but dependent on the values of the levels. Thus, their values must be generated.**

**2. Leading Indicator Models**

**In this class of model, we set £**

_{1}=Ω_{0}=0 to obtain:

**C**

_{t}= Ω_{1}Y_{t-1}+ U_{t (4)}

**Here, we simply exclude the current value (Y**

_{t}) of the explanatory and the influence of the variable in form of dynamic specification. We inevitably create an economic problem (via the exclusion of possibly relevant explanatory variable) in effort to solve a statistical one. This problem is all the more serious if it turns out that the regressor used in the specification is after all, not truly a leading indicator of the dependent variable.

**3. Growth Rate Models**

**To derive the growth rate model from the above ARDL model , we set £**

_{1}=1 and Ω_{1}=- Ω_{0}(Ω_{1}+Ω_{0}).We obtain the growth model as:

**∆ C**

_{t}= £_{1}∆Y_{t }+ U_{t (5)}

**Here again, the valuable information on the level of the variable is lost. However, the lost is counterbalanced by the gain arising from the fact that there are economic variables better captured by growth rate models. It can also be called first difference.**

**4. Distributed Lag Models (DLM)**

**To derive a**DLM model, we set £

_{1 }in the ARDL model to zero i.e £_{1}=0.we would obtain

**C**

_{t}= Ω_{0}Y_{t }+ Ω_{1}Y_{t-1 }+ U_{t (6)}

**The DLM represents an improvement of over static regression and the leading indicator models.**

**5. Partial Adjustment Models (PAM)**

**To obtain the PAM, we set Ω**

_{1}=0 and get :

**C**

_{t}= £ C_{t -1 }+ Ω_{0}Y_{t }+U_{ t (7)}

**This is one of the most popular and most widely used models in econometric analysis.**

**6. Dead Start Models (DSM)**

**In DSM, we set Ω**

_{0 }in the ARDL model equal to zero, then the DSM is as follows:

**C**

_{t}= £_{1}C_{t -1 }+ Ω_{0}Y_{t-1}+ U_{t (8)}

**The current values of the explanatory variable in the specification of the model are eliminated. The fit of the DSMs can be quite poor since the level of the variable are excluded as explanatory variables.**

**7. Common Factor Model**

**In common factor model we set Ω**

_{1}=-Ω_{0}£_{1}_{, }then we obtain_{ :}

**C**

_{t}= Ω_{0}Y_{t}+e_{t,}e_{t}= Ω_{1 }e_{t-1}+ U_{t (9)}

**8. Error Correction Models (ECM)**

**To obtain ECM, we set Ω**

_{0}+Ω_{1}+ £_{1}=1 and then obtain:

**∆C**

_{t}=Ω_{0}∆Y_{t}+ (Ω_{1 }-1)(C_{t -1 }-Y_{t-1}) +U_{t (10)}

_{ }

**Note that in ECMs.**

**(i) The specification is not in levels, but in differences.**

**(ii) Y and C are linearly combined i.e (Ω**

_{1 }-1) (C_{t -1 }-Y_{t-1}).

**In ECM cointegration relationship are captured and they contain stationary series at first difference. It captures both long run and short run relationship expressed in an econometric model.**

_{How to build an econometric model}

_{ }Kerem Tuzcuoglu in his comment on how to build a simple econometric model, wrote down these steps:

**· First of all, other than X, think about what other factors can affect Y, call them W, the control variables. Gather a data set containing {Y, X, W}.**

**· Plot your data to see whether there is any anomaly in the data. For instance, whether there is any outlier or whether the data are concentrated in two different regions etc. (remember that the data should be independent and identically distributed).**

**· Then proceed further by plotting Y vs X, try to understand whether the relationship between Y and X is linear, quadratic, log-linear, or log-log, etc. Perform the necessary transformations. For instance, if you see a curvature relationship between Y and X, then you might want to add X and X2X2 in your analysis. Also this should economically make sense — like a decreasing returns to scale type of a reasoning.**

**· Regress Y on X. Check the significance of X and whether your initial assertion holds. Then, add W variables to the regression, and see whether your assertion still holds.**

**· These are pretty much the main steps. You can increase the confidence of people on your results by obtaining the residuals and plotting them for instance. Remember, errors should be independent and identically distributed too. Or plot the residuals against X to see whether there is any heteroscedasticty etc.**

**A large part of econometrics is the study of methods for selecting models, estimating them, and carrying out inference (Wikipedia).**

**REFERENCES**

**Gujarati, D.N., & Porter, D.C.(2009).Basic Econometrics (5**

^{th}ed.). Boston: McGraw Hill.

**Iganiga, B.O.(2009). Introductory Econometrics: Made Easy. Antitop Books.P.151-158.**

**Pesaran, H.P.(1990). “Econometrics” . The New Palgrave Dictionary of Econometrics(2**

^{nd}ed.). Abstract.

**Pesaran , M.H.(1989).”Econometrics”. The New Palgrave :A Dictionary of Econometrics,V2,P.8(pp.8-22). Reprinted in J.Eat well et al., eds.(1990). Econometrics: The New Palgrave, P.1(pp.1-34),Abstract (2008 revision by J.Geweke, J. Horowitz, and H.P Pesaran).**

**Sims,C.A. (1980) . Macroeconomics and Reality. Econometrica.48(1):1-48.**

**Spanos, A,(2008). “Statistics and Economics”, The New Palgrave Dictionary ofEconomic,2**

^{nd}Edition.Abstract.

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