A Primer on Regression Analysis: a Consumption Function Example

A Primer on Regression Analysis: A Consumption Function Example

The example below should be a little familiar to you from econ 004. Consumption accounts for about 70% of GDP and is thus, very much studied by economists and other economic actors interested in understanding and predicting economic activity. In econ 004 you should, at the very least, recall that disposable income and the level of consumption are tightly related, that is, if we have data on disposable income, then we can make pretty good guesses as to the level of consumption. You should also recall that consumption is also influenced by other factors as well. In what follows, we develop a fairly realistic model of consumption, and then we simplify it when interpreting the empirical results.

Consumption Function

where:

Yd is personal disposable income

WSM is wealth in the stock market

WRE is wealth in real estate

r is the real interest rate

EX is the exchange rate where an increase implies the dollar is appreciating

CC is consumer confidence

If we used all the variables (above) to predict consumption, the regression equation will take the following form:

The ai’s are sensitivity parameters. They tell us which direction and by how much consumption is affected by changes in each of the variables. For instance, a1 is the marginal propensity to consume (MPC), and tells us how sensitive consumption is to changes in disposable income.[1]

Empirical Results – The Consumption Function

The set up: I estimate a consumption function that includes all the arguments: above except for the exchange rate. The purpose of this example is to get you familiar with the usefulness and interpretation of these empirical results.

Important features of regression output:

R2 represents the fit of the model; the higher the R2, the better the fit. The maximum value for R2 is 1.00 and the minimum value is zero.

t-stats; if the absolute value of the t-stat exceeds 2.00, then we say that the associated variable ‘belongs’ in the regression. t-stats basically test whether or not a coefficient is significantly different than zero. If the t-stat exceeds two, then the coefficient is said to be ‘statistically different than zero.’

Coefficient interpretation: We are typically interested in the sign of the coefficient (i.e., is it consistent with economic theory) as well as the size (this has to do with economic significance). Example: the MPC (a1) in the equation above should be positive, close to one, and significant.[2]

Empirical Results on the consumption function

Equation estimated

C = a0 + a1 Yd + a2 r + a3 WSM + a4 WRE + a5 CC

Priors:

a1 is the marginal propensity to consume and should be somewhere around 0.9 in value and very significant (high t-statistic) since we know there does exist a tight relationship between consumption and disposable income.

a2 should be negative since the lower the real rate of interest, the less in pays to save (i.e., consume!).

a3 should be positive and significant – i.e., the wealth effect in terms of stock market wealth.

a4 should be positive and significant – i.e., the wealth effect in terms of real estate wealth. Note also that the claim is that a4 should be greater than a3, that is, dollar for dollar, the wealth effect in real estate is great than the wealth effect in stocks since changes in the former (real estate wealth) are perceived by economic agents to be more permanent and stable than the latter (changes in stock market wealth ,’here today, gone tomorrow.’

a5 should be positive, the more confident you are, the more you consume!

Also, the overall fit should be quite good, since we know that there is tight relationship between C and Yd

Regression Output: 1977Q3 – 2006Q2

C = -115 + .788(Yd) – 10.486(r) + .032(WSM) + .078(WRE) + .516(CC)

[1] You should recall the marginal propensity to consume from your principles classes and also that the value of the MPC plays a critical role in determining the “multiplier” and thus, determining, in part, the ‘power’ of monetary and fiscal policy.

[2] Most believe that the MPC in the US is quite high relative to the rest of the world with the empirical estimates somewhere around 0.9, which implies that for each $1.00 increase in disposable income, consumption will rise by 90 cents with the remaining 10 cents being saved.