Economic analysis is about identifying systematic patterns in data that may confirm or deny theory, and which can help decisionmakers see the best way forward. The key word is ‘systematic‘. In the real world (or the real business world) there is variation everywhere. Somebody is seen to raise price and sell more, to cut price and sell less, to increase market share and go bankrupt, to issue loads of debt and get rich…. everything is possible and can be documented on a case by case basis. The question is whether this or that case or data set provides generalizable insight, or is just an interesting situation. Is there something generalizable in what we see, to guide our future actions, or is it just circumstantially interesting?

The isolation of common, systematic patterns of behavior and building a body theory to guide thinking is what the practice of economics is about. The theory of demand is a good example, even though the simple demand curve is built with unrealistic simplifying assumptions. but, so much of what is at the essence of firm managerial behavior is captured by the simple demand concept— firms invest a lot trying to shift out and to tilt their demand curve— advertising, loyalty building investments, product differentiation, eliminating rivals, —all tend to shift and tilt demand so that profits can be enhanced by creating the power to raise price and increase revenue.

So, we hear that relations with Cuba will soon be normalized, or that the price of oil continues to fall, or see a report that shows that one of our stores is doing much better than the others. What are these data telling us that we can use?

Seeing VARIATION is a managers opportunity to learn more about  WHY things are happening, and to move beyond the level of introspection that most people operate—understanding WHAT is happening. Yes, knowing WHAT is happening is important. But learning can be deeper is we can understand WHY it is happening— this allows the manager to generalize and craft incentives, to craft marketing programs, to take advantage of knowledge of WHY the variation is occurring.

So, if we see variation across stores in our chain, or variation in time of day our sales are happening— then we can do economic analysis of various types to see if there are any systematic patterns in the variation we see. Lets say we are interested in understanding more about why our chain of hospitals has variation in revenues per bed. What is driving this?  Using SCATTER PLOTS, we can quickly checkout some possibilities of systematic differences going on among our hospitals. Below, we show the variation across the chain in terms of ADMISSIONS per CAPITA on the vertical axis. And, we show how many beds there are per capita in the places we have hospitals.

supply-induced-demand

What this shows is that in places with more beds, we have more admissions per capita. This odd” relationship is something we call “supply induced demand”. Where there are more beds, people get more hospital care. This, of course suggests that the use of hospitals is not based on “scientific need for care”. Rather, hospitalization is quite discretionary for many kinds of problems– and doctors tend to develop practice styles of admitting more patients when there are more beds available. Note, that the pattern doesnt exist for the red line– showing the admissions for Hip Fractures— such admits dont vary at all with bed availability— if you have a fractured hip, admission is necessary. No discretion.

So, we learn a little about why admissions (and revenue) may vary across our sites because of the patterns we see. Looking at patterns across types of patients (age, gender, insurance status) or across types of service (maternity, surgery, outpatient, etc.) of community characteristic (rural, suburban, inner city) may help understand the WHY we are experiencing variation in our performance. This can be done by scatter plots, or tables of central tendency across groupings of our hospitals (averages or medians).

Sometimes we may suspect some systematic differences, and want to confirm it. We use statistical analysis to do that. Is the “pattern” we see more than just a possibility of the”noisy” variation in our data?

“What produces health” is a good illustration of massive variation in results–and the need to understand what underlying patters are driving most of that variation? Lots of things. At core, individual people decide how healthy they want to be, and what they might do day-to-day to achieve that aim. Not everyone cares the same about current and future health, and have different priorities for deploying their scare money and time resources toward their health aims. SOme people dont care about health at all—others fret daily about it. And, since “good health” can have a large effect on our future (in many ways) it is often sort of an “investment” —whereby people commit resources now in order to earn benefit6s later in life. But, of course, all people dont want to wait to recieve future benefits of spending money and time now to get healthier . So, the situation is that we have massive differences among us in our aim of how healthy we want to be, and consequently, differences in how healthy we are!

As policy analysts, thinking of improving the “bang for the buck” we get for our health spending (and also trying to make our health system more fair as well) we must understand the systematic patterns of the underlying health drivers. What makes us healthier? We do that by estimating “health production functions” using regression. We use data on individuals or groups of individuals to estimate algorithms like:

Health status  =  a  +  b (age) + c (gender) + d (educ level) + e (spending on health)  + other                                                                                                                                                        factors

And, we use theory to guide us as to what factors are potentially important influences on individual health choices.

Testing Theory with Data

The issue in all such theory is developing tests of this behavior using real world data, where assumptions don’t match the simplifying theory. How to cope? Well, most theories are tested by using regression approaches, where assumptions are proxied by ‘controlling’ the extraneous influences on the simple price-quantity relationship. How to control for the effect of varying income, or effects of different competitor prices, or areas with more or less competition, etc. Essentially regression allows these ‘other influences on the key relationship of interest’ to be ‘held constant’ by including them in the regression model, which separately estimates their partial effects on the dependent variable. So, when i am interested in the effect of age group on the hospital charges, i can “control’ for severity by including it in the model as well. The regression coefficients are each partial estimates of the change in the dependent variable associated with a one unit change in the particular independent variable, holding constant the effects of other independent variables. So the effect of age group on charges holds constant the effect of severity on charges. This technique is the way we create measured effects of one variable on another, with simplifying assumptions about other relevant influences. Economic theory guides us on what these other influences might be, so we can be sure to include them in our economic analysis.

Our purpose is to determine if there are underlying patterns of relationships that confirm (or not) theories about how firms behave—- and our interest in these systematic patterns is to expand the body of knowledge that guides our understanding of how firms behave when hiring executives. For example, lets say we are interested in whether hospitals discriminate in their hiring behavior of managers. We would need to study the patterns of hiring managers to discover if discrimination is occurring. Do firms behave as if they were responding to labor market theories, or others? What we’d be interested in is whether the place-to-place variations in the propensity to hire minority managers is related to:
1. variations in the hospital marketplace itself— are there systematic differences in hiring when hospitals are larger, or when the industry is more/less competitive, or when the missions of hospitals are different (ownership and teaching status).
2. variations in the supply of workers—- are their systematic variations in minority hiring associated with the % of population that is minority, or the relative #s of minorites with college degrees,
3. variations in region. we know there are more and less willingness to accept minority managers in different regions of the country, and in urban and ruiral areas.

WE WOULD EXPECT SUCH relationships to explain some portion of the observed variation in minority hiring— but is there anything left unexplained? If yes, what could be the systematic explanation for it?

One theory that is relevant here is the theory of discrimination (Gary Becker, Nobel prize winner). His theory says that business may discriminate (racial, gender, ethnic, etc.) if they have customers or employees who prefer it. Said another way, discrimination is the sacrifice in potential profitability to achieve some non economic end. Discrimination is such an end. While stockholders may not like it, sometimes caving to pressure from other employees or customers (or other stakeholders) may be done. So, it may be that unexplained variations in minority hiring may reflect this or other systematic (but unmeasured) influences.

So, looking at the article, how important are supply forces in explaining place-to-place variations in % minority managers? How important are hospital market factors? Can You think of other things that would have been good to measure to help understand the variation?

Regression is a way of understanding the empirical relationship between variables, where the relationship is expressed in the form of an estimated linear equation developed from data. A demand curve, for example, would be such a line, relating the quantity bought and the price. Often, regression is a way of testing hypotheses about the relationship between 2 or more variables(one is called dependent variable, others are called independent variables). Multiple regression is a way of testing for these two way relationships when the effects of other variables is being held constant. Note: even though we call the variables dependent and independent, regression does not test for causality between the two variables. It tests for association between them (similar to correlation). The cause-effect relationship (eg the directions of causality) between two variables is possible to infer from theory, or from patterns of complex statistical results.

Regression analysis essentially displays the scatter of data between two variables

regression

If we were doing a cost analysis and trying to determine fixed costs and marginal costs we could use regression. So, if we had data on each year of operations, or each month of operations, or each day we would use those data to specify the following equation:

Total costs = A + b (Volume of output)

A would be an estimate of what costs would be if volume were 0. This is fixed costs! The coefficient “b” is the estimated change in costs when we add (or subtract) one unit of output—this is the marginal costs. Average costs can easily be calculated in the raw data.

If we had some other variable that changes and might help explain why the cost/volume relationship might “shift” during the data period we are studying, then we could add it to the regression. For example if we had a monthly data set on costs and volumes we might want to note (and control for) the fact that the last 6 data points were from a time when we were open in the evenings (and the other data points were from times when we were not open in the evenings). So our regression is going to be

Total costs = A + b (V) + c (evening open) this =1 for the last 6 months, and = 0 otherwise)

So, A and B still mean what we said, though their values may change a bit with the new model. The coefficient “c” tells us how our total costs change (per month, per day or per week depending on what our data is) when we are open evenings, compared to our costs when we are not open in the evenings.

Regression coefficient estimates have important interpretations in economics. In the above example of the cost regression, we might have an estimated equation

Total monthly cost = 50000 + 100(V) +   20 (evening open)

the coefficient estimate “b” is interpreted at the change in total cost when we increase the volume (V) by one unit (this might be the number of clients we saw each day. This is called variable (or marginal) cost. The 50000 is the estimate of fixed costs (which we incur independent of the volume we produce.

In the case where we might have estimated a demand curve, such as

Quantity sold =   A   +   b (price)   +   c (household income in 000s)   +   d(competitor’s price)

We could estimate it from data and get:

Quantity sold   = 500   –   15 (price)     +   20 (income )   +   30 (competitors price)

1. What this means is that if our price was zero, and income were zero and the competitors price was zero we would sell 500 units (silly, but it tells us where the demand curve crosses the horizontal axis (eg where out price is zero)
2. It says that if we increase our price by $1, we’d sell 15 fewer units of the product (other stuff like income and competitors prices staying constant)
3. it says that if household income were 1000 higher on average, we could expect to sell 20 more units (other things held constant, like our price and competitor prices. Is this a normal or an inferior good?
4. it says that if competitors lowered their prices by $1 we would sell 30 fewer units (other things the same. Are they a substitute or a complement?

Excel does regression. Look under tools to see if you can add in the “data analysis” add in. If you have it, find it under the Data tab. You can do descriptive analyses and other things with “data analysis”, but scroll down to regression. It will ask you to highlight the column of data that represents the dependent variable. Usually it is best to highlight the name of the variable and all the data in the column. Then it will ask to designate the independent variable, and you do the same thing. And then make sure to check the box that says “include the data labels” (because you highlighted the data labels too). If you have 2 or more independent variables you can include them in the model. You do this by putting all these variables in adjacent columns, and highlighting all of them in one fell swoop. Note, excel will not do regression if cells are missing data, or if there is a non numeric value in a cell (a comma, etc.). You will get some message when you push the regression button to run the model, and you’ll have to locate the problem, and possibly through away one of the observations.

i did a simple regression on excel and have attached it below. The data set below was used to do a regression to understand the factors associated with the size of hospital bills across a bunch of patients (eg the variable called “ charges “). I ran a regression analysis to test three relationships:

1. Does age matter to the size of bill
2. Does the category of the age matter
3. Does severity of the diagnosis/procedure matter

basically what i did in excel was to go to the data analysis, regression page–and key in the cell location of the dependent variable (in this case, hospital charges for 39 patients) which variation in i was trying to explain by 3 independent variables — age, age category, severity. I had to put these variables in adjacent columns and key in the cell locations of these three things. In the regressions they came out as three unnamed variables since i neglected to select the column heading.

I explain the results on the sheet showing what excel produced as results—much of which is not important at this stage of the game.

You could use the data set to create a different model , say one that used only patient severity as a independent variable to explain charges.

regression2

Forecasting
Almost every person finds themselves in a situation in their job where they have to make a projection or forecast of sales revenue, or cash needs or something. Every business plan requires this sort of thing. While this is an area where deep technical skills exist, it is also an area which requires MBAs to be equipped to do a serviceable job (when the job can’t afford to hire an expensive consultant) and to understand the limits of their work.